Sharp general local estimates for dyadic-like maximal operators and related Bellman functions

DOI10.1016/j.aim.2008.09.010zbMath1178.42021OpenAlexW2058314442MaRDI QIDQ960570

Antonios D. Melas

Publication date: 22 December 2008

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2008.09.010

zbMATH Keywords

maximal operatorBellman functionHady operator

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (21)

The Bellman function of the dyadic maximal operator in connection with the dyadic Carleson imbedding theorem ⋮ Dyadic-like maximal operators on \(L \log L\) functions ⋮ Sharp integral inequalities for the dyadic maximal operator and applications ⋮ Local lower norm estimates for dyadic maximal operators and related Bellman functions ⋮ A sharp two-weight estimate for the maximal operator under a bump condition ⋮ Best constants for a family of Carleson sequences ⋮ On A_p–A_q weighted estimates for maximal operators ⋮ Survey article: Bellman function method and sharp inequalities for martingales ⋮ Extremizers and sharp weak-type estimates for positive dyadic shifts ⋮ Sharp \(L^{p,\infty}\to L^q\) estimates for the dyadic-like maximal operators ⋮ On weak type inequalities for dyadic maximal functions ⋮ An alternative approach to sharp $L^1$ estimates for the dyadic maximal operator ⋮ The geometry of the dyadic maximal operator ⋮ A SPLITTING PROCEDURE FOR BELLMAN FUNCTIONS AND THE ACTION OF DYADIC MAXIMAL OPERATORS ON ⋮ A sharp integral rearrangement inequality for the dyadic maximal operator and applications ⋮ Sharp Lorentz-norm estimates for dyadic-like maximal operators ⋮ The $\boldsymbol {\mathrm {BMO}}\boldsymbol {\rightarrow }\boldsymbol {\mathrm {BLO}}$ action of the maximal operator on $\boldsymbol \alpha $-trees ⋮ An eigenfunction stability estimate for approximate extremals of the Bellman function for the dyadic maximal operator on 𝐿^{𝑝} ⋮ Sharp weighted inequalities for harmonic maximal operators ⋮ Extremal sequences for the Bellman function of three variables of the dyadic maximal operator related to Kolmogorov’s inequality ⋮ Sharp local lower 𝐿^{𝑝}-bounds for Dyadic-like maximal operators

Cites Work

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• Dyadic-like maximal operators on \(L \log L\) functions
• Monge-Ampère equations and Bellman functions: the dyadic maximal operator
• The Bellman functions of dyadic-like maximal operators and related inequalities
• Sharp results in the integral-form John–Nirenberg inequality
• Bellman Function and the $H^1-BMO$ Duality
• The Bellman functions and two-weight inequalities for Haar multipliers
• The sharp constant in the reverse Hölder inequality for Muckenhoupt weights
• The Bellman functions for a certain two-weight inequality: A case study
• Monge--Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems
• Sharp Maximal Inequalities for Conditionally Symmetric Martingales and Brownian Motion

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