Burkholder meets Gundy: Bellman function method for general operators on martingales

DOI10.1016/J.AIM.2022.108746zbMath1502.42020arXiv2107.06384OpenAlexW4287078449MaRDI QIDQ2094606

Yanyan Li

Publication date: 8 November 2022

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

Full work available at URL: https://arxiv.org/abs/2107.06384

zbMATH Keywords

Walsh systemHaar transformRubio de Francia inequalityBurkholder methodGundy theorem

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Martingales and classical analysis (60G46) Operator theory and harmonic analysis (47B90)

Cites Work

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• On Permutations of Lacunary Intervals
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• Littlewood–Paley–Rubio de Francia inequality for the Walsh system
• A Decomposition for $L^1$-Bounded Martingales
• Sharp estimates of integral functionals on classes of functions with small mean oscillation

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