Existence of convolution maximizers in \(L_p(\mathbb{R}^n)\) with kernels from Lorentz spaces

DOI10.1007/s10958-023-06278-4arXiv2208.08783OpenAlexW4366988519MaRDI QIDQ6147568

Sergey Yu. Sadov

Publication date: 1 February 2024

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.08783

zbMATH Keywords

convolutionHardy-Littlewood-Sobolev inequalitybest constantstight sequenceweak \(L_p\) spaceexistence of extremizer

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Best constants in approximation theory (41A44)

Cites Work

• Estimates for translation invariant operators in \(L^p\) spaces
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• An existence criterion for maximizers of convolution operators in \(L_1(\mathbb{R}^n)\)
• Classical Fourier Analysis
• On maximizers of a convolution operator in -spaces
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