Dyadic-like maximal operators on integrable functions and Bellman functions related to Kolmogorov’s inequality

DOI10.1090/S0002-9947-09-04872-7zbMath1194.42026OpenAlexW2049041133MaRDI QIDQ3550547

Eleftherios N. Nikolidakis, Antonios D. Melas

Publication date: 31 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-09-04872-7

zbMATH Keywords

maximal functionBellman functionKolmogorov's inequalitydyadic-like maximal operators

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (15)

The Bellman function of the dyadic maximal operator in connection with the dyadic Carleson imbedding theorem ⋮ The Bellman function of the dyadic maximal operator related to Kolmogorov's inequality ⋮ Dyadic-like maximal operators on \(L \log L\) 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 ⋮ Sharp weak type inequalities for the dyadic maximal operator ⋮ Sharp \(L^{p,\infty}\to L^q\) estimates for the dyadic-like maximal operators ⋮ Sharp weak-type estimates for the dyadic-like maximal operators ⋮ The geometry of the dyadic maximal operator ⋮ A SPLITTING PROCEDURE FOR BELLMAN FUNCTIONS AND THE ACTION OF DYADIC MAXIMAL OPERATORS ON ⋮ Extremal problems related to maximal dyadic-like operators ⋮ The $\boldsymbol {\mathrm {BMO}}\boldsymbol {\rightarrow }\boldsymbol {\mathrm {BLO}}$ action of the maximal operator on $\boldsymbol \alpha $-trees ⋮ Extremal sequences for the Bellman function of three variables of the dyadic maximal operator related to Kolmogorov’s inequality

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• The Bellman functions and two-weight inequalities for Haar multipliers
• Best Constants for Uncentred Maximal Functions
• 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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