The Helson-Szegoe theorem and A//p-functions for Brownian motion and several variables

DOI10.1016/0022-1236(80)90022-1zbMath0505.60056OpenAlexW2047845973MaRDI QIDQ1836444

Nicholas Th. Varopoulos

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90022-1

zbMATH Keywords

Carleson corona theoremconformal Brownian martingalesHelson-Szegoe theorem

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Martingales and classical analysis (60G46) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items

Carleson measures on product domains and 2-parameter Brownian martingales, Some typical ideal in a uniform algebra, A decomposition for Hardy martingales II, A Decomposition for Hardy Martingales III, The algebra of bounded holomorphic martingales, Measures of Carleson Type on Filtrated Probability Spaces and the Corona Theorem on Complex Brownian Spaces, On the Algebra of Bounded Holomorphic Martingales, Interpolation for Hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales, Holomorphic martingales and interpolation between Hardy spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic functions and logmodular Banach algebras
• Wolff's proof of the corona theorem
• A probabilistic proof of the Garnett-Jones theorem on BMO
• Distribution function inequalities for martingales
• Conjugate function theory in weak\(^*\) Dirichlet algebras
• A problem in prediction theory
• Interpolations by bounded analytic functions and the corona problem
• Multiple Wiener integral
• On functions of bounded mean oscillation
• Weighted norm inequalities for maximal functions and singular integrals
• Characterisations of $H^1$ by singular intetgral transforms on martingales and $\mathsf{R}^n$
• Bounded Analytic Functions
• A sub-regularity inequality for conjugate systems on local fields
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
• The distance in BMO to \(L^\infty\)