Equivalent definitions of dyadic Muckenhoupt and reverse Hölder classes in terms of Carleson sequences, weak classes, and comparability of dyadic \(L \log L\) and \(A_\infty\) constants

DOI10.4171/RMI/812zbMath1325.42030arXiv1201.0520OpenAlexW2170888209MaRDI QIDQ2256071

Alexander Reznikov, Oleksandra V. Beznosova

Publication date: 19 February 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.0520

zbMATH Keywords

Bellman functionsharp estimatesreverse Hölder classeselliptic PDECarleson sequencesdyadic Muckenhoupt classes

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Harmonic analysis in several variables (42B99) Harmonic analysis and PDEs (42B37)

Related Items (9)

Perfect dyadic operators: weighted \(T(1)\) theorem and two weight estimates ⋮ On the \(A_\infty\) conditions for general bases ⋮ Wasserstein distance and the rectifiability of doubling measures. I ⋮ A fractional Muckenhoupt-Wheeden theorem and its consequences ⋮ Sharp reverse Hölder property for \(A_\infty\) weights on spaces of homogeneous type ⋮ Best constants for a family of Carleson sequences ⋮ On Two Weight Estimates for Dyadic Operators ⋮ Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution ⋮ A new quantitative two weight theorem for the Hardy-Littlewood maximal operator

Cites Work

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• The sharp \(A_p\) constant for weights in a reverse-Hölder class
• The theory of weights and the Dirichlet problem for elliptic equations
• Summation conditions on weights
• The \(Tb\)-theorem on non-homogeneous spaces.
• On the operator \({\mathcal L}(f)=f\log|f|\)
• Sharp weighted estimates for dyadic shifts and the \(A_2\) conjecture
• An estimate for weighted Hilbert transform via square functions
• The Ap-Ainfty inequality for general Calderon-Zygmund operators
• The Bellman functions and two-weight inequalities for Haar multipliers
• Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities

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