Convolution inequalities in Lorentz spaces

DOI10.1007/s00041-010-9159-9zbMath1235.44012OpenAlexW2117048785MaRDI QIDQ719696

Sergey Yu. Tikhonov, E. D. Nursultanov

Publication date: 11 October 2011

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-010-9159-9

zbMATH Keywords

Lorentz spaceconvolution operatorYoung-O'Neil inequality

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) Integral operators (47G10)

Related Items (18)

Refinements of some limit Hardy-type inequalities via superquadracity ⋮ On the convolution operator in Morrey spaces ⋮ Some properties of convolution in symmetric spaces and approximate identity ⋮ Some new sharp limit Hardy-type inequalities via convexity ⋮ Estimates for decreasing rearrangements of convolution and coverings of cones ⋮ Convolution inequalities in weighted Lorentz spaces: case 0<q<1 ⋮ O'Neil type convolution inequalities in Lorentz spaces ⋮ Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries ⋮ O'NEIL-TYPE INEQUALITIES FOR CONVOLUTIONS IN ANISOTROPIC LORENTZ SPACES ⋮ Convolution in rearrangement-invariant spaces defined in terms of oscillation and the maximal function ⋮ Sharp weighted convolution inequalities and some applications ⋮ Fourier transforms on weighted amalgam-type spaces ⋮ Weighted convolution inequalities for radial functions ⋮ Weighted norm inequalities for convolution and Riesz potential ⋮ On some fixed point theorems in abstract duality pairs ⋮ Norm inequalities for convolution operators ⋮ Weighted Fourier inequalities in Lebesgue and Lorentz spaces ⋮ Reduction theorems for weighted integral inequalities on the cone of monotone functions

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