Sharp Weak-Type Inequality for the Haar System, Harmonic Functions and Martingales

DOI10.4064/ba62-2-7zbMath1303.60034OpenAlexW2010057144MaRDI QIDQ2926670

Adam Osȩkowski

Publication date: 3 November 2014

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/b4ad61dd85a62139bf80c48189036ed2dfd545e8

zbMATH Keywords

harmonic functionHaar systemmartingalebest constantdifferential subordination

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martingales with continuous parameter (60G44)

Related Items (3)

A weak-\(L^\infty\) inequality for weakly dominated martingales with applications to Haar shift operators ⋮ Weak-\( L^\infty\) inequality for non-symmetric martingale transforms and Haar system ⋮ Sharp weighted weak type \((\infty, \infty)\) inequality for differentially subordinate martingales

Cites Work

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• Boundary value problems and sharp inequalities for martingale transforms
• A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional
• Differential subordination and strong differential subordination for continuous-time martingales and related sharp inequalities
• A sharp weak type $(p,p)$ inequality $(p>2)$ for martingale transforms and other subordinate martingales
• Martingale Transforms
• A Remarkable Series of Orthogonal Functions (I)

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