Fractional smoothness in \(L^p\) with Dunkl weight and its applications

DOI10.1134/S0001434619090232zbMath1435.42007arXiv1812.04946OpenAlexW2981814993WikidataQ126986625 ScholiaQ126986625MaRDI QIDQ2291212

Valeriĭ I. Ivanov, Dmitry Gorbachev

Publication date: 30 January 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04946

zbMATH Keywords

convolution\(K\)-functionalmodulus of smoothnessgeneralized translation operatorDunkl transformDunkl Laplacian

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear operators on function spaces (general) (47B38) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Inverse theorems in approximation theory (41A27) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (3)

Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications ⋮ Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Bernstein inequality in \(L^p\) on the line with power weight for \(p>0\)

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