A weak-type inequality for differentially subordinate harmonic functions

DOI10.1090/S0002-9947-98-02259-4zbMath0913.31001OpenAlexW1560938502MaRDI QIDQ4211070

Changsun Choi

Publication date: 10 September 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02259-4

zbMATH Keywords

harmonic measureharmonic functionsdifferential subordinationBurkholder's inequalityweak-type Kolmogorov inequality

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martingales and classical analysis (60G46) Conjugate functions, conjugate series, singular integrals (42A50) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (7)

Sharp weak-type inequalities for differentially subordinated martingales ⋮ The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ Sharp maximal inequalities for the moments of martingales and non-negative submartingales ⋮ A sharp weak-type bound for Itô processes and subharmonic functions ⋮ A sharp one-sided bound for the Hilbert transform ⋮ A generalized Kolmogorov inequality for the Hilbert transform ⋮ Sharp \(L^p\) bound for holomorphic functions on the unit disc

Cites Work

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• Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms
• Stochastically recursive sequences and their generalizations
• On the best values of the constants in the theorem of M. Riesz, Zygmund and Kolmogorov
• On the Weak Type (1, 1) Inequality for Conjugate Functions

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