Dyadic-like maximal operators on \(L \log L\) functions

DOI10.1016/j.jfa.2009.06.005zbMath1173.42011OpenAlexW1520848838MaRDI QIDQ841492

Antonios D. Melas

Publication date: 17 September 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.06.005

zbMATH Keywords

maximal functionBellman functionsdyadic maximal function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (16)

The Bellman function of the dyadic maximal operator in connection with the dyadic Carleson imbedding theorem ⋮ Local lower norm estimates for dyadic maximal operators and related Bellman functions ⋮ The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ A sharp two-weight estimate for the maximal operator under a bump condition ⋮ On A_p–A_q weighted estimates for maximal operators ⋮ Extremizers and sharp weak-type estimates for positive dyadic shifts ⋮ Sharp \(L^{p,\infty}\to L^q\) estimates for the dyadic-like maximal operators ⋮ Sharp Lorentz estimates for dyadic-like maximal operators and related Bellman functions ⋮ Sharp general local estimates for dyadic-like maximal operators and related Bellman functions ⋮ An alternative approach to sharp $L^1$ estimates for the dyadic maximal operator ⋮ A SPLITTING PROCEDURE FOR BELLMAN FUNCTIONS AND THE ACTION OF DYADIC MAXIMAL OPERATORS ON ⋮ Sharp Lorentz-norm estimates for dyadic-like maximal operators ⋮ 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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• Boundary value problems and sharp inequalities for martingale transforms
• Monge-Ampère equations and Bellman functions: the dyadic maximal operator
• Sharp general local estimates for dyadic-like maximal operators and related Bellman functions
• The Bellman functions of dyadic-like maximal operators and related inequalities
• Sharp results in the integral-form John–Nirenberg inequality
• A SHARP $L^{\lowercase{p}}$ INEQUALITY FOR DYADIC $A_{1}$ WEIGHTS IN $\mathbb{R}^{\lowercase{n}}$
• Dyadic-like maximal operators on integrable functions and Bellman functions related to Kolmogorov’s inequality
• The Bellman functions and two-weight inequalities for Haar multipliers
• The sharp constant in the reverse Hölder inequality for Muckenhoupt weights
• Monge--Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems
• Note on the class LlogL

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