Stefanie Petermichl
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Stefanie Petermichl has a total of 25 co-authors. Here are the top co-authors by number of shared publications:
- Komla Domelevo
Institut für Mathematik , 9190 Universität Würzburg , Emil-Fischer-Straße 40, 97074 Würzburg , Germany
6 shared publications - Alexander Volberg
Department of Mathematics, MSU, East Lansing, USA
3 shared publications - Christoph Kriegler
Université Clermont Auvergne, CNRS, LMBP, Clermont-Ferrand, France
2 shared publications Komla Domelevo
Inst Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany
2 shared publications- Odí Soler i Gibert
Universitat Politècnica de Catalunya-BarcelonaTech (UPC), Barcelona, Spain
2 shared publications - Sergei Treil
Department of Mathematics, Brown University, Providence, RI, USA
2 shared publications
Latest Publications
- Open Access
- 14 October 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH
- p. 737-760
The matrix 𝐀₂ conjecture
This survey begins with the history of modern weighted theory and its consequences for the Hilbert transform with scalar weight. It proceeds through further development in the area that leads to the counterexample to the famous matrix ${\mathbf{A}}\_{2}$ conjecture.- 14 October 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH
- p. 737-760
Open AccessThe matrix 𝐀₂ conjecture
This survey begins with the history of modern weighted theory and its consequences for the Hilbert transform with scalar weight. It proceeds through further development in the area that leads to the counterexample to the famous matrix ${\mathbf{A}}\_{2}$ conjecture. - Open Access
- 4 March 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Oberwolfach Reports
- Vol. 22 (4) , 2843-2916
Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis
The purpose of this workshop is the strengthening of the interaction between the fields of Stochastic Partial Differential Equations (SPDEs), Backward Stochastic Differential Equations (BSDEs), and Harmonic and Functional Analysis. We focus on the essential role of analytic techniques (including function spaces, weighted inequalities, and A_{p} -weights) in solving problems in critical stochastic settings. Special topics include SPDEs in critical spaces, regularization by noise, singular SPDEs, quadratic and nonlocal BSDEs.
- 4 March 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Oberwolfach Reports
- Vol. 22 (4) , 2843-2916
Open AccessRecent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis
The purpose of this workshop is the strengthening of the interaction between the fields of Stochastic Partial Differential Equations (SPDEs), Backward Stochastic Differential Equations (BSDEs), and Harmonic and Functional Analysis. We focus on the essential role of analytic techniques (including function spaces, weighted inequalities, and A_{p} -weights) in solving problems in critical stochastic settings. Special topics include SPDEs in critical spaces, regularization by noise, singular SPDEs, quadratic and nonlocal BSDEs.
- Open Access
- 28 November 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (1) , 24
From the Classical Fefferman-Kenig-Pipher $A_{\infty }$ Inequality to Its Matrix Version and BeyondThe main goal of this article is the celebration of Jill Pipher, who was postdoctoral mentor of the author and continued to be her mentor. We review the Fefferman-Kenig-Pipher $$A_{\infty }$$ inequality for scalar weights using the heat extension. We transition from a Bellman function proof in the heat setting to its dyadic scalar version. From here, we transition to the matrix analog of this inequality. The matrix result itself is implicit in papers by Treil and Volberg. In this text we present a more classical looking Bellman proof with derivative estimates resulting in the dyadic convexity estimate. We also prove via Bellman function an unrelated general embedding sum whose scalar version has been used in sharp paraproduct estimates. In the matrix case this inequality holds in the sense of operators and it appears to be new.- 28 November 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (1) , 24
Open AccessFrom the Classical Fefferman-Kenig-Pipher $A_{\infty }$ Inequality to Its Matrix Version and BeyondThe main goal of this article is the celebration of Jill Pipher, who was postdoctoral mentor of the author and continued to be her mentor. We review the Fefferman-Kenig-Pipher $$A_{\infty }$$ inequality for scalar weights using the heat extension. We transition from a Bellman function proof in the heat setting to its dyadic scalar version. From here, we transition to the matrix analog of this inequality. The matrix result itself is implicit in papers by Treil and Volberg. In this text we present a more classical looking Bellman proof with derivative estimates resulting in the dyadic convexity estimate. We also prove via Bellman function an unrelated general embedding sum whose scalar version has been used in sharp paraproduct estimates. In the matrix case this inequality holds in the sense of operators and it appears to be new. - 25 April 2025
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
Continuous sparse domination and dimensionless weighted estimates for the Bakry–Riesz vector
We present a fundamentally new proof of the dimensionless boundedness of the Bakry–Riesz vector on manifolds with bounded geometry, with our proof being new even in the Euclidean setting. Our proof has the significant advantage that it allows for a much stronger conclusion than previous arguments, namely that of some new dimensionless weighted estimates with optimal exponent. Part of the importance of this task lies in the novelty of the techniques: we develop the self-similarity argument known as “sparse domination” in the setting of uniformly integrable càdlàg Hilbert space valued martingales and extend the domination to a process with infinite memory. We provide a range of optimal weighted estimates and weak type estimates for these stochastic processes. Previous geometric Riesz transform estimates relied on Bellman functions and did not provide this range of weighted estimates. The development of sparse domination in this probabilistic setting and its use for high-dimensional problems is new.- 25 April 2025
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
Continuous sparse domination and dimensionless weighted estimates for the Bakry–Riesz vector
We present a fundamentally new proof of the dimensionless boundedness of the Bakry–Riesz vector on manifolds with bounded geometry, with our proof being new even in the Euclidean setting. Our proof has the significant advantage that it allows for a much stronger conclusion than previous arguments, namely that of some new dimensionless weighted estimates with optimal exponent. Part of the importance of this task lies in the novelty of the techniques: we develop the self-similarity argument known as “sparse domination” in the setting of uniformly integrable càdlàg Hilbert space valued martingales and extend the domination to a process with infinite memory. We provide a range of optimal weighted estimates and weak type estimates for these stochastic processes. Previous geometric Riesz transform estimates relied on Bellman functions and did not provide this range of weighted estimates. The development of sparse domination in this probabilistic setting and its use for high-dimensional problems is new.- Open AccessThe matrix $A_2$ conjecture fails, i.e. $3/2>1$We show that the famous matrix $A_2$ conjecture is false: the norm of the Hilbert Transform in the space $L^2(W)$ with matrix weight $W$ is estimated below by $C[W]_{{A}_2}^{3/2}$.Open AccessThe matrix $A_2$ conjecture fails, i.e. $3/2>1$We show that the famous matrix $A_2$ conjecture is false: the norm of the Hilbert Transform in the space $L^2(W)$ with matrix weight $W$ is estimated below by $C[W]_{{A}_2}^{3/2}$.
- Open Access
Boundedness of Journé operators with matrix weights
We develop a biparameter theory for matrix weights and provide various biparameter matrix-weighted bounds for Journ\'e operators as well as other central operators under the assumption of the product matrix Muckenhoupt condition. In particular, we provide a complete theory for biparameter Journ\'e operator bounds on matrix-weighted $L^2$ spaces. We also achieve bounds in the general case of matrix-weighted $L^p$ spaces, for $1 < p < \infty$ for paraproduct-free Journ\'e operators. Finally, we expose an open problem involving a matrix-weighted Fefferman--Stein inequality, on which our methods rely in the general setting of matrix-weighted bounds for arbitrary Journ\'e operators and $p \neq 2.$Open AccessBoundedness of Journé operators with matrix weights
We develop a biparameter theory for matrix weights and provide various biparameter matrix-weighted bounds for Journ\'e operators as well as other central operators under the assumption of the product matrix Muckenhoupt condition. In particular, we provide a complete theory for biparameter Journ\'e operator bounds on matrix-weighted $L^2$ spaces. We also achieve bounds in the general case of matrix-weighted $L^p$ spaces, for $1 < p < \infty$ for paraproduct-free Journ\'e operators. Finally, we expose an open problem involving a matrix-weighted Fefferman--Stein inequality, on which our methods rely in the general setting of matrix-weighted bounds for arbitrary Journ\'e operators and $p \neq 2.$ - 1 July 2023
- Published by Universitat Autonoma de Barcelona in Publicacions Matemàtiques
- Vol. 67 (2) , 661-685
Dyadic lower little BMO estimates
- 1 July 2023
- Published by Universitat Autonoma de Barcelona in Publicacions Matemàtiques
- Vol. 67 (2) , 661-685
Dyadic lower little BMO estimates
- 16 April 2021
- Published by Springer Nature in Mathematische Annalen
- Vol. 381 (3-4) , 1137-1195
$H^{\infty }$ calculus for submarkovian semigroups on weighted $L^2$ spaces- 16 April 2021
- Published by Springer Nature in Mathematische Annalen
- Vol. 381 (3-4) , 1137-1195
$H^{\infty }$ calculus for submarkovian semigroups on weighted $L^2$ spaces- 26 February 2020
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 148 (6) , 2433-2446
Discrete Hilbert transform à la Gundy–Varopoulos
We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic processes considered have jump components. The stochastic representation of the function and that of its Hilbert transform are under differential subordination and orthogonality relation with respect to the sharp bracket of quadratic covariation. This illustrates the Cauchy–Riemann relations of analytic functions in this setting. This result is inspired by the seminal work of Gundy and Varopoulos on stochastic representation of the Hilbert transform in the continuous setting.
- 26 February 2020
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 148 (6) , 2433-2446
Discrete Hilbert transform à la Gundy–Varopoulos
We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic processes considered have jump components. The stochastic representation of the function and that of its Hilbert transform are under differential subordination and orthogonality relation with respect to the sharp bracket of quadratic covariation. This illustrates the Cauchy–Riemann relations of analytic functions in this setting. This result is inspired by the seminal work of Gundy and Varopoulos on stochastic representation of the Hilbert transform in the continuous setting.
- 1 December 2019
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 582, 452-466
Failure of the matrix weighted bilinear Carleson embedding theorem
- 1 December 2019
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 582, 452-466
Failure of the matrix weighted bilinear Carleson embedding theorem