Estimates for imaginary powers of Laplace operator in variable Lebesgue spaces and applications

DOI10.3103/S1068362314050045zbMath1319.42012MaRDI QIDQ2345383

Alberto Fiorenza, Amiran Gogatishvili, Tengiz Kopaliani

Publication date: 22 May 2015

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

zbMATH Keywords

Mellin transformwave equationLaplace operatorsingular integral operatorsvariable exponent Lebesgue spacesspherical maximal functionimaginary powers

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) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Wave equation (35L05) Laplace transform (44A10) Harmonic analysis and PDEs (42B37)

Related Items (2)

Maximal multiplier operators in \(L^{p(\cdot)}(\mathbb{R}^n)\) spaces ⋮ On interpolation of reflexive variable Lebesgue spaces on which the Hardy-Littlewood maximal operator is bounded

Cites Work

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• Some remarks on the Hardy-Littlewood maximal function on variable \(L^p\) spaces
• On maximal functions
• Maximal functions: Spherical means
• On weighted estimates for Stein's maximal function

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