Harmonic AnalysisCopyright (c) 2023 Washington University in St. Louis All rights reserved.
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis
Recent Events in Harmonic Analysisen-usWed, 21 Jun 2023 16:54:36 PDT3600Quantitative two weight estimates for dyadic operators
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/10
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/10Thu, 21 Jul 2016 15:30:00 PDT
In this talk we present quantitative two weight estimates for the dyadic paraproduct and the dyadic square function. We compare known results of Holmes, Lacey, and Wick for the paraproduct when both weights are in $A_2$ involving Bloom's BMO, and a different Carleson condition when the weights are in joint $A_2$ plus an additional Carleson condition on the weights (both necessary and sufficient conditions for a dual two-weight boundedness of the dyadic square function). We compare these to necessary and sufficient testing conditions for each particular dyadic paraproduct when viewed as a well-localized operator in the sense of Nazarov, Treil, and Volberg.
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Maria Cristina PereyraMatrix $A_p$ weights, degenerate Sobolev spaces, and mappings of finite distortion.
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/9
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/9Fri, 22 Jul 2016 16:00:00 PDT
We study degenerate Sobolev spaces where the degeneracy is controlled by a matrix A_p weight. We prove that the classical Meyers-Serrin theorem, H = W, holds in this setting. As applications we prove partial regularity results for weak solutions of degenerate p-Laplacian equations, and in particular for mappings of finite distortion.
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Kabe MoenBoundedness of commutators and H1-BMO duality in the two matrix weighted setting
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/8
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/8Fri, 22 Jul 2016 15:30:00 PDT
In this talk we discuss the two matrix weighted boundedness of commutators with any of the Riesz transforms in terms of a natural two matrix weighted BMO space. Furthermore, we identify this BMO space when $p =2$ as the dual of a natural two matrix weighted $H^1$ space and discuss some consequences.
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Joshua IsralowitzTwo-Weight Inequalities for Commutators
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/7
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/7Fri, 22 Jul 2016 15:00:00 PDT
In this talk we discuss commutators with Calderon-Zygmund operators in the two-weight setting. In particular, we extend a one-dimensional result of S. Bloom for the Hilbert transform to n-dimensional Calderon-Zygmund operators, and discuss some natural extensions to iterated commutators and commutators with Riesz potentials.
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Irina HolmesWeighted Estimates for Multilinear Dyadic Operators and Their Commutators
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/6
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/6Fri, 22 Jul 2016 14:30:00 PDT
Multilinear dyadic paraproducts and Haar multipliers arise naturally in the decomposition of the pointwise product of two or more functions. I will present weighted estimates for these operators, as well as their commutators with dyadic BMO functions.
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Ishwari KunwarWeak factorization of Hardy spaces and characterization of BMO spaces in the Bessel setting and applications
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/5
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/5Thu, 21 Jul 2016 17:00:00 PDT
It is well-known that the classical Hardy space $H^p$, $0
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Ji LiPersistence as a spectral property
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/4
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/4Thu, 21 Jul 2016 16:00:00 PDT
A Gaussian stationary sequence is a random function f: Z --> R, for which any vector (f(x_1), ..., f(x_n)) has a centered multi-normal distribution and whose distribution is invariant to shifts. Persistence is the event of such a random function to remain positive on a long interval [0,N]. Estimating the probability of this event has important implications in engineering , physics, and probability. However, though active efforts to understand persistence were made in the last 50 years, until recently, only specific examples and very general bounds were obtained. In the last few years, a new point of view simplifies the study of persistence, namely - relating it to the spectral measure of the process. In this work we use this point of view to develop new spectral and analytical methods in order to study the persistence in cases where the spectral measure is 'small' near zero. This talk is based on Joint work with Naomi Feldheim and Ohad Feldheim.
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Shahaf NitzanA Two-Weight Inequality for Essentially Well Localized Operators
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/3
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/3Fri, 22 Jul 2016 17:00:00 PDT
Nazarov, Treil and Volberg first introduced and characterized the two-weight boundedness of well localized operators. In this talk, we introduce a generalization of these operators, called essentially well localized operators, and obtain necessary and sufficient conditions to characterize their boundedness between $L^2(\mathbb{R}^n,u)$ and $L^2(\mathbb{R}^n,v)$ for general Radon measures $u$ and $v$.
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Philip BengeMean Holder Continuity, Area Integral Means and Extremal Problems
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/2
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/2Thu, 21 Jul 2016 15:00:00 PDT
I will discuss mean H\"{o}lder continuity conditions for functions in Bergman spaces and the relation of these conditions with the growth of area integral means of derivatives of analytic functions. I will also discuss a result about mean Holder continuity of solutions of certain linear extremal problems in Bergman spaces that is similar to a result of Khavinson, McCarthy, and Shapiro (but with improved Holder exponent for $1 < p < 2$). I will indicated some applications of this result.
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Tim FergusonSharp Weighted Bounds for the Bergman Projection and Related Operators on $A^2(\mathbb{B}^n)$
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/1
https://openscholarship.wustl.edu/iwota2016/special/HarmonicAnalysis/1Thu, 21 Jul 2016 14:30:00 PDT
Using techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Bergman spaces on the unit ball in $\mathbb{C}^n$. The estimates are in terms of the Bekolle-Bonami constant of the weight. This generalizes results of Pott-Reguera to several variables and to a more general class of operators. This is joint work with Brett Wick and Edgar Tchoundja.
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Robert Rahm