Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups

DOI10.1007/s11118-016-9571-0zbMath1360.60092arXiv1506.01208OpenAlexW2413029379MaRDI QIDQ345045

Daesung Kim

Publication date: 25 November 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01208

zbMATH Keywords

Littlewood-Paley \(g\)-functionfractional integralHardy-Littlewood-Sobolev inequalityHardy-Littlewood-Paley inequalityMarkovian semigroupmartingale transforms

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Markov semigroups and applications to diffusion processes (47D07) Applications of stochastic analysis (to PDEs, etc.) (60H30) Martingales and classical analysis (60G46) Inequalities involving derivatives and differential and integral operators (26D10) Pseudodifferential operators (47G30)

Related Items (3)

Generalized fractional integral operators based on symmetric Markovian semigroups with application to the Heisenberg group ⋮ Hardy–Littlewood–Sobolev type inequalities associated with the Weinstein operator ⋮ Hardy-Stein identity for non-symmetric Lévy processes and Fourier multipliers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp logarithmic inequalities for Riesz transforms
• Sharp constants in several inequalities on the Heisenberg group
• Boundary value problems and sharp inequalities for martingale transforms
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Extremals of functionals with competing symmetries
• Hardy-Littlewood theory for semigroups
• Aspects of probabilistic Littlewood-Paley theory
• Littlewood-Paley inequality for a diffusion satisfying the logarithmic Sobolev inequality and for the Brownian motion on a Riemannian manifold with boundary
• The foundational inequalities of D. L. Burkholder and some of their ramifications
• Martingale transforms and \(L^p\)-norm estimates of Riesz transforms on complete Riemannian manifolds
• Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality
• Sharp Martingale and Semimartingale Inequalities
• Space-time Brownian motion and the Beurling-Ahlfors transform
• Martingale Transforms and Related Singular Integrals
• On Certain Convolution Inequalities
• Heating of the Ahlfors–Beurling operator, and estimates of its norm
• On singular integral and martingale transforms
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• An “alternierende Verfahren” for general positive operators

This page was built for publication: Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups