María Cristina Pereyra
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
María Cristina Pereyra has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- Jean Carlo Moraes
Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
3 shared publications - Ji Li
School of Mathematical and Physical Sciences, Macquarie University, NSW, Australia
3 shared publications - Carlos Pérez
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain
2 shared publications - Daewon Chung
Department of Mathematics and Statistics MSC01 1115, University of New Mexico, Albuquerque, New Mexico 87131-0001
2 shared publications - Lesley A. Ward
University of South Australia
2 shared publications Amir R. Nafchi
1 shared publication
Latest Publications
- 31 October 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (1) , 1-31
Two-weight estimates for the square function and t-Haar multipliers
- 31 October 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (1) , 1-31
Two-weight estimates for the square function and t-Haar multipliers
- Open Access
Las funciones booleans y el lema de Bonami
In this expository article, we study the relation between the boolean functions and the hypercontractivity theorems of Aline Bonami. We focus on the social choice theory, and present some of the most important results in the area, such as the Friedgut-Kalai-Naor (FKN) and the Kahn-Kalai-Linial (KKL) theorems, and the famous Fourier Entropy/Influence conjecture. -- En este artículo expositivo estudiamos la relación entre las funciones booleanas y los teoremas de hipercontractividad de Aline Bonami. Nos concentramos en la teoría de la elección social, y presentamos algunos de los resultados más importantes en el área como los teoremas de Friedgut-Kalai-Naor (FKN) y de Kahn-Kalai-Linial (KKL), y la famosa conjetura Entropíıa de Fourier/Influencia.
Open AccessLas funciones booleans y el lema de Bonami
In this expository article, we study the relation between the boolean functions and the hypercontractivity theorems of Aline Bonami. We focus on the social choice theory, and present some of the most important results in the area, such as the Friedgut-Kalai-Naor (FKN) and the Kahn-Kalai-Linial (KKL) theorems, and the famous Fourier Entropy/Influence conjecture. -- En este artículo expositivo estudiamos la relación entre las funciones booleanas y los teoremas de hipercontractividad de Aline Bonami. Nos concentramos en la teoría de la elección social, y presentamos algunos de los resultados más importantes en el área como los teoremas de Friedgut-Kalai-Naor (FKN) y de Kahn-Kalai-Linial (KKL), y la famosa conjetura Entropíıa de Fourier/Influencia.
- 24 October 2020
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 31 (9) , 8947-8978
Geometric Characterizations of Embedding Theorems: For Sobolev, Besov, and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type—via Orthonormal Wavelets
- 24 October 2020
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 31 (9) , 8947-8978
Geometric Characterizations of Embedding Theorems: For Sobolev, Besov, and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type—via Orthonormal Wavelets
- Open Access
Circular Convolution and Product Theorem for Affine Discrete Fractional Fourier Transform
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of the discrete fractional Fourier transform, its applications in digital communications have been elusive. The convolution property of the discrete Fourier transform plays a vital role in designing multi-carrier modulation systems. Here we report a closed-form affine discrete fractional Fourier transform and we show the circular convolution property for it. The proposed approach is versatile and generalizes the discrete Fourier transform and can find applications in Fourier based signal processing tools.
Open AccessCircular Convolution and Product Theorem for Affine Discrete Fractional Fourier Transform
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of the discrete fractional Fourier transform, its applications in digital communications have been elusive. The convolution property of the discrete Fourier transform plays a vital role in designing multi-carrier modulation systems. Here we report a closed-form affine discrete fractional Fourier transform and we show the circular convolution property for it. The proposed approach is versatile and generalizes the discrete Fourier transform and can find applications in Fourier based signal processing tools.
- 27 November 2019
- Published by Springer Nature
- p. 159-239
Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution
- 27 November 2019
- Published by Springer Nature
- p. 159-239
Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution
- Open Access
Dyadic harmonic analysis and weighted inequalities: the sparse revolution
We will introduce the basics of dyadic harmonic analysis and how it can be used to obtain weighted estimates for classical Calder\'on-Zygmund singular integral operators and their commutators. Harmonic analysts have used dyadic models for many years as a first step towards the understanding of more complex continuous operators. In 2000 Stefanie Petermichl discovered a representation formula for the venerable Hilbert transform as an average (over grids) of dyadic shift operators, allowing her to reduce arguments to finding estimates for these simpler dyadic models. For the next decade the technique used to get sharp weighted inequalities was the Bellman function method introduced by Nazarov, Treil, and Volberg, paired with sharp extrapolation by Dragi\v{c}evi\'c et al. Other methods where introduced by Hyt\"onen, Lerner, Cruz-Uribe, Martell, P\'erez, Lacey, Reguera, Sawyer, Uriarte-Tuero, involving stopping time and median oscillation arguments, precursors of the very successful domination by positive sparse operators methodology. The culmination of this work was Tuomas Hyt\"onen's 2012 proof of the $A_2$ conjecture based on a representation formula for any Calder\'on-Zygmund operator as an average of appropriate dyadic operators. Since then domination by sparse dyadic operators has taken central stage and has found applications well beyond Hyt\"onen's $A_p$ theorem. We will survey this remarkable progression and more in these lecture notes.Open AccessDyadic harmonic analysis and weighted inequalities: the sparse revolution
We will introduce the basics of dyadic harmonic analysis and how it can be used to obtain weighted estimates for classical Calder\'on-Zygmund singular integral operators and their commutators. Harmonic analysts have used dyadic models for many years as a first step towards the understanding of more complex continuous operators. In 2000 Stefanie Petermichl discovered a representation formula for the venerable Hilbert transform as an average (over grids) of dyadic shift operators, allowing her to reduce arguments to finding estimates for these simpler dyadic models. For the next decade the technique used to get sharp weighted inequalities was the Bellman function method introduced by Nazarov, Treil, and Volberg, paired with sharp extrapolation by Dragi\v{c}evi\'c et al. Other methods where introduced by Hyt\"onen, Lerner, Cruz-Uribe, Martell, P\'erez, Lacey, Reguera, Sawyer, Uriarte-Tuero, involving stopping time and median oscillation arguments, precursors of the very successful domination by positive sparse operators methodology. The culmination of this work was Tuomas Hyt\"onen's 2012 proof of the $A_2$ conjecture based on a representation formula for any Calder\'on-Zygmund operator as an average of appropriate dyadic operators. Since then domination by sparse dyadic operators has taken central stage and has found applications well beyond Hyt\"onen's $A_p$ theorem. We will survey this remarkable progression and more in these lecture notes. - Open Access
Atomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type
We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\"onen and their underlying reference dyadic grids. However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry out this program, we introduce product $(p,q)$-atoms on $\widetilde{X}$ and product atomic Hardy spaces $H^{p,q}_{{\rm at}}(\widetilde{X})$. As consequences of the atomic decomposition of $H^p(\widetilde{X})$, we show that for all $q > 1$ the product atomic Hardy spaces coincide with the product Hardy spaces, and we show that the product Hardy spaces are independent of the particular choices of both the wavelet bases and the reference dyadic grids. Likewise, the product Carleson measure spaces ${\rm CMO}^p(\widetilde{X})$, the bounded mean oscillation space ${\rm BMO}(\widetilde{X})$, and the vanishing mean oscillation space ${\rm VMO}(\widetilde{X})$, as defined by Han, Li, and Ward, are also independent of the particular choices of both wavelets and reference dyadic grids.Open AccessAtomic decomposition of product Hardy spaces via wavelet bases on spaces of homogeneous type
We provide an atomic decomposition of the product Hardy spaces $H^p(\widetilde{X})$ which were recently developed by Han, Li, and Ward in the setting of product spaces of homogeneous type $\widetilde{X} = X_1 \times X_2$. Here each factor $(X_i,d_i,\mu_i)$, for $i = 1$, $2$, is a space of homogeneous type in the sense of Coifman and Weiss. These Hardy spaces make use of the orthogonal wavelet bases of Auscher and Hyt\"onen and their underlying reference dyadic grids. However, no additional assumptions on the quasi-metric or on the doubling measure for each factor space are made. To carry out this program, we introduce product $(p,q)$-atoms on $\widetilde{X}$ and product atomic Hardy spaces $H^{p,q}_{{\rm at}}(\widetilde{X})$. As consequences of the atomic decomposition of $H^p(\widetilde{X})$, we show that for all $q > 1$ the product atomic Hardy spaces coincide with the product Hardy spaces, and we show that the product Hardy spaces are independent of the particular choices of both the wavelet bases and the reference dyadic grids. Likewise, the product Carleson measure spaces ${\rm CMO}^p(\widetilde{X})$, the bounded mean oscillation space ${\rm BMO}(\widetilde{X})$, and the vanishing mean oscillation space ${\rm VMO}(\widetilde{X})$, as defined by Han, Li, and Ward, are also independent of the particular choices of both wavelets and reference dyadic grids. - Open Access
On two weight estimates for dyadic operators
We provide a quantitative two weight estimate for the dyadic paraproduct $\pi_b$ under certain conditions on a pair of weights $(u;v)$ and $b$ in $Carl_{u,v}$, a new class of functions that we show coincides with BMO when $u = v \in A^d_2$. We obtain quantitative two weight estimates for the dyadic square function and the martingale transforms under the assumption that the maximal function is bounded from $L_2(u)$ into $L_2(v)$ and $v \in RH^d_1$. Finally we obtain a quantitative two weight estimate from $L_2(u)$ into $L_2(v)$ for the dyadic square function under the assumption that the pair $(u; v)$ is in joint $A^d_2$ and $u^{-1} \in RH^d_1$, this is sharp in the sense that when $u = v$ the conditions reduce to $u \in A^d_2$ and the estimate is the known linear mixed estimate.Open AccessOn two weight estimates for dyadic operators
We provide a quantitative two weight estimate for the dyadic paraproduct $\pi_b$ under certain conditions on a pair of weights $(u;v)$ and $b$ in $Carl_{u,v}$, a new class of functions that we show coincides with BMO when $u = v \in A^d_2$. We obtain quantitative two weight estimates for the dyadic square function and the martingale transforms under the assumption that the maximal function is bounded from $L_2(u)$ into $L_2(v)$ and $v \in RH^d_1$. Finally we obtain a quantitative two weight estimate from $L_2(u)$ into $L_2(v)$ for the dyadic square function under the assumption that the pair $(u; v)$ is in joint $A^d_2$ and $u^{-1} \in RH^d_1$, this is sharp in the sense that when $u = v$ the conditions reduce to $u \in A^d_2$ and the estimate is the known linear mixed estimate. - Open Access
Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type
We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next we focus on spaces $X$ of homogeneous type in the sense of Coifman and Weiss, where we use these Haar functions to define a discrete square function, and hence to define dyadic versions of the function spaces $H^1(X)$ and ${\rm BMO}(X)$. In the setting of product spaces $\widetilde{X} = X_1 \times \cdots \times X_n$ of homogeneous type, we show that the space ${\rm BMO}(\widetilde{X})$ of functions of bounded mean oscillation on $\widetilde{X}$ can be written as the intersection of finitely many dyadic ${\rm BMO}$ spaces on $\widetilde{X}$, and similarly for $A_p(\widetilde{X})$, reverse-H\"older weights on $\widetilde{X}$, and doubling weights on $\widetilde{X}$. We also establish that the Hardy space $H^1(\widetilde{X})$ is a sum of finitely many dyadic Hardy spaces on $\widetilde{X}$, and that the strong maximal function on $\widetilde{X}$ is pointwise comparable to the sum of finitely many dyadic strong maximal functions. These dyadic structure theorems generalize, to product spaces of homogeneous type, the earlier Euclidean analogues for ${\rm BMO}$ and $H^1$ due to Mei and to Li, Pipher and Ward.Open AccessHaar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type
We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next we focus on spaces $X$ of homogeneous type in the sense of Coifman and Weiss, where we use these Haar functions to define a discrete square function, and hence to define dyadic versions of the function spaces $H^1(X)$ and ${\rm BMO}(X)$. In the setting of product spaces $\widetilde{X} = X_1 \times \cdots \times X_n$ of homogeneous type, we show that the space ${\rm BMO}(\widetilde{X})$ of functions of bounded mean oscillation on $\widetilde{X}$ can be written as the intersection of finitely many dyadic ${\rm BMO}$ spaces on $\widetilde{X}$, and similarly for $A_p(\widetilde{X})$, reverse-H\"older weights on $\widetilde{X}$, and doubling weights on $\widetilde{X}$. We also establish that the Hardy space $H^1(\widetilde{X})$ is a sum of finitely many dyadic Hardy spaces on $\widetilde{X}$, and that the strong maximal function on $\widetilde{X}$ is pointwise comparable to the sum of finitely many dyadic strong maximal functions. These dyadic structure theorems generalize, to product spaces of homogeneous type, the earlier Euclidean analogues for ${\rm BMO}$ and $H^1$ due to Mei and to Li, Pipher and Ward. - Open Access
Weighted estimates for dyadic paraproducts and t-Haar multipiers with complexity (m,n)
We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m,n), for m and n positive integers. We will use the ideas developed by Nazarov and Volberg to prove that the weighted L^2(w)-norm of a paraproduct with complexity (m,n) associated to a function b\in BMO, depends linearly on the A_2-characteristic of the weight w, linearly on the BMO-norm of b, and polynomially in the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct (the one with complexity (0,0)). Also we prove that the L^2-norm of a t-Haar multiplier for any t and weight w depends on the square root of the C_{2t}-characteristic of w times the square root of the A_2-characteristic of w^{2t} and polynomially in the complexity (m,n), recovering a result of Beznosova for the (0,0)-complexity case.
Open AccessWeighted estimates for dyadic paraproducts and t-Haar multipiers with complexity (m,n)
We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m,n), for m and n positive integers. We will use the ideas developed by Nazarov and Volberg to prove that the weighted L^2(w)-norm of a paraproduct with complexity (m,n) associated to a function b\in BMO, depends linearly on the A_2-characteristic of the weight w, linearly on the BMO-norm of b, and polynomially in the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct (the one with complexity (0,0)). Also we prove that the L^2-norm of a t-Haar multiplier for any t and weight w depends on the square root of the C_{2t}-characteristic of w times the square root of the A_2-characteristic of w^{2t} and polynomially in the complexity (m,n), recovering a result of Beznosova for the (0,0)-complexity case.