Emiel Lorist
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Emiel Lorist has a total of 22 co-authors. Here are the top co-authors by number of shared publications:
- Mark Veraar
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
9 shared publications - Andrei K. Lerner
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
5 shared publications - Alex Amenta
Mathematisches Institut, Universität Bonn, Bonn, Germany
4 shared publications - Sheldy Ombrosi
Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense (Spain), Madrid, Spain
3 shared publications - Sheldy Ombrosi
Universidad Nacional del Sur
2 shared publications - Timo S. Hanninen
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
2 shared publications
Latest Publications
- Open Access
Operator-valued Fourier multipliers of bounded s-variation
In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability condition on its bounded $s$-variation seminorms over dyadic intervals. The exponents $r$ and $s$ reflect the relationship between the geometric properties of the underlying Banach spaces (type and cotype) and the boundedness of Fourier multiplier operators. As our main tool we prove a weighted vector-valued variational Carleson inequality and deduce an estimate of Littlewood--Paley--Rubio de Francia type.Open AccessOperator-valued Fourier multipliers of bounded s-variation
In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability condition on its bounded $s$-variation seminorms over dyadic intervals. The exponents $r$ and $s$ reflect the relationship between the geometric properties of the underlying Banach spaces (type and cotype) and the boundedness of Fourier multiplier operators. As our main tool we prove a weighted vector-valued variational Carleson inequality and deduce an estimate of Littlewood--Paley--Rubio de Francia type. - Open Access
- 4 December 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 454
Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains
- 4 December 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 454
Open AccessFunctional calculus on weighted Sobolev spaces for the Laplacian on rough domains
- Open Access
Optimization algorithms for Carleson and sparse collections of sets
Carleson and sparse collections of sets play a central role in dyadic harmonic analysis. We employ methods from optimization theory to study such collections. First, we present a strongly polynomial algorithm to compute the Carleson constant of a collection of sets, improving on the recent approximation algorithm of Rey. Our algorithm is based on submodular function minimization. Second, we provide an algorithm showing that any Carleson collection is sparse, achieving optimal dependence of the respective constants and thus providing a constructive proof of a result of Hänninen. Our key insight is a reformulation of the duality between the Carleson condition and sparseness in terms of the duality between the maximum flow and the minimum cut in a weighted directed graph.
Open AccessOptimization algorithms for Carleson and sparse collections of sets
Carleson and sparse collections of sets play a central role in dyadic harmonic analysis. We employ methods from optimization theory to study such collections. First, we present a strongly polynomial algorithm to compute the Carleson constant of a collection of sets, improving on the recent approximation algorithm of Rey. Our algorithm is based on submodular function minimization. Second, we provide an algorithm showing that any Carleson collection is sparse, achieving optimal dependence of the respective constants and thus providing a constructive proof of a result of Hänninen. Our key insight is a reformulation of the duality between the Carleson condition and sparseness in terms of the duality between the maximum flow and the minimum cut in a weighted directed graph.
- Open Access
- 7 June 2024
- Published by Springer Nature in Semigroup Forum
- Vol. 108 (3) , 594-625
Strongly Kreiss bounded operators in UMD Banach spaces
In this paper we give growth estimates for $$\Vert T^n\Vert $$ for $$n\rightarrow \infty $$ in the case T is a strongly Kreiss bounded operator on a $${{\,\textrm{UMD}\,}}$$ Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and $$L^p$$ -spaces, but also intermediate $${{\,\textrm{UMD}\,}}$$ spaces such as non-commutative $$L^p$$ -spaces and variable Lebesgue spaces.- 7 June 2024
- Published by Springer Nature in Semigroup Forum
- Vol. 108 (3) , 594-625
Open AccessStrongly Kreiss bounded operators in UMD Banach spaces
In this paper we give growth estimates for $$\Vert T^n\Vert $$ for $$n\rightarrow \infty $$ in the case T is a strongly Kreiss bounded operator on a $${{\,\textrm{UMD}\,}}$$ Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and $$L^p$$ -spaces, but also intermediate $${{\,\textrm{UMD}\,}}$$ spaces such as non-commutative $$L^p$$ -spaces and variable Lebesgue spaces. - Open Access
- 2 May 2024
- Published by Springer Nature in Journal of Fourier Analysis and Applications
- Vol. 30 (3) , 1-25
Extrapolation of Compactness on Banach Function Spaces
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator T in the weighted Lebesgue scale and the compactness of T in the unweighted Lebesgue scale yields compactness of T on a very general class of Banach function spaces. As our main new tool, we prove various characterizations of the boundedness of the Hardy-Littlewood maximal operator on such spaces and their associate spaces, using a novel sparse self-improvement technique. We apply our main results to prove compactness of the commutators of singular integral operators and pointwise multiplication by functions of vanishing mean oscillation on, for example, weighted variable Lebesgue spaces.
- 2 May 2024
- Published by Springer Nature in Journal of Fourier Analysis and Applications
- Vol. 30 (3) , 1-25
Open AccessExtrapolation of Compactness on Banach Function Spaces
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator T in the weighted Lebesgue scale and the compactness of T in the unweighted Lebesgue scale yields compactness of T on a very general class of Banach function spaces. As our main new tool, we prove various characterizations of the boundedness of the Hardy-Littlewood maximal operator on such spaces and their associate spaces, using a novel sparse self-improvement technique. We apply our main results to prove compactness of the commutators of singular integral operators and pointwise multiplication by functions of vanishing mean oscillation on, for example, weighted variable Lebesgue spaces.
- Open Access
- 15 March 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 306 (4) , 1-32
Bloom weighted bounds for sparse forms associated to commutators
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner–Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón–Zygmund operators, the previously known quantitative Bloom bounds are not sharp for the second and higher order commutators.
- 15 March 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 306 (4) , 1-32
Open AccessBloom weighted bounds for sparse forms associated to commutators
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner–Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón–Zygmund operators, the previously known quantitative Bloom bounds are not sharp for the second and higher order commutators.
- Open Access
- 22 November 2023
- Published by Elsevier in Indagationes Mathematicae
- Vol. 35 (2) , 247-268
Banach function spaces done right
- 22 November 2023
- Published by Elsevier in Indagationes Mathematicae
- Vol. 35 (2) , 247-268
Open AccessBanach function spaces done right
- Open Access
Euclidean structures and operator theory in Banach spaces
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $\Gamma$ on a Hilbert space. Our assumption on $\Gamma$ is expressed in terms of $\alpha$-boundedness for a Euclidean structure $\alpha$ on the underlying Banach space $X$. This notion is originally motivated by $\mathcal{R}$- or $\gamma$-boundedness of sets of operators, but, for example, any operator ideal from the Euclidean space $\ell^2_n$ to $X$ defines such a structure. Therefore, our method is quite flexible. Conversely we show that $\Gamma$ has to be $\alpha$-bounded for some Euclidean structure $\alpha$ to be representable on a Hilbert space. By choosing the Euclidean structure $\alpha$ accordingly, we get a unified and more general approach to classical factorization and extension theorems. Furthermore we use these Euclidean structures to build vector-valued function spaces and define an interpolation method based on these spaces, which has formulations modelled after both the real and the complex interpolation method. Using our representation theorem we prove a transference principle for sectorial operators on a Banach space, enabling us to extend Hilbert space results for sectorial operators to the Banach space setting. We define generalizations of the classical square function estimates in $L^p$-spaces and establish, via the $H^\infty$-calculus, a version of Littlewood-Paley theory and associated spaces of fractional smoothness for a rather large class of sectorial operators. Our results for sectorial operators lead to some sophisticated counterexamples.Open AccessEuclidean structures and operator theory in Banach spaces
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $\Gamma$ on a Hilbert space. Our assumption on $\Gamma$ is expressed in terms of $\alpha$-boundedness for a Euclidean structure $\alpha$ on the underlying Banach space $X$. This notion is originally motivated by $\mathcal{R}$- or $\gamma$-boundedness of sets of operators, but, for example, any operator ideal from the Euclidean space $\ell^2_n$ to $X$ defines such a structure. Therefore, our method is quite flexible. Conversely we show that $\Gamma$ has to be $\alpha$-bounded for some Euclidean structure $\alpha$ to be representable on a Hilbert space. By choosing the Euclidean structure $\alpha$ accordingly, we get a unified and more general approach to classical factorization and extension theorems. Furthermore we use these Euclidean structures to build vector-valued function spaces and define an interpolation method based on these spaces, which has formulations modelled after both the real and the complex interpolation method. Using our representation theorem we prove a transference principle for sectorial operators on a Banach space, enabling us to extend Hilbert space results for sectorial operators to the Banach space setting. We define generalizations of the classical square function estimates in $L^p$-spaces and establish, via the $H^\infty$-calculus, a version of Littlewood-Paley theory and associated spaces of fractional smoothness for a rather large class of sectorial operators. Our results for sectorial operators lead to some sophisticated counterexamples. - Open Access
Bloom weighted bounds for sparse forms associated to commutators
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner-Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón--Zygmund operators, the previously known quantitative Bloom weighted estimates are not sharp for the second and higher order commutators.
Open AccessBloom weighted bounds for sparse forms associated to commutators
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner-Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón--Zygmund operators, the previously known quantitative Bloom weighted estimates are not sharp for the second and higher order commutators.
- 30 April 2023
- Published by Springer Nature in Mathematische Annalen
- Vol. 388 (4) , 4053-4082
BMO with respect to Banach function spaces
- 30 April 2023
- Published by Springer Nature in Mathematische Annalen
- Vol. 388 (4) , 4053-4082
BMO with respect to Banach function spaces