Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

DOI10.1007/s00013-012-0362-6zbMath1246.46034OpenAlexW2017259024MaRDI QIDQ412022

Yoshihiro Mizuta, Tetsu Shimomura, Yoshihiro Sawano, Eiichi Nakai

Publication date: 3 May 2012

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-012-0362-6

zbMATH Keywords

space of homogeneous typeMusielak-Orlicz spacevariable exponentGagliardo-Nirenberg inequalitygeneralized Riesz potentials

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)

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Asymptotic behavior of solutions to the drift-diffusion equation with critical dissipation ⋮ Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation ⋮ Generalized fractional integral operators on variable exponent Morrey spaces of an integral form ⋮ Brezis-van Schaftingen-Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo-Nirenberg inequalities ⋮ Gagliardo representation of norms of ball quasi-Banach function spaces ⋮ Biographical Sketch of Professor Eiichi Nakai ⋮ Applications of Littlewood-Paley theory for \(\dot{B}_\sigma\)-Morrey spaces to the boundedness of integral operators ⋮ Gagliardo--Nirenberg inequality for generalized Riesz potentials of functions in Musielak--Orlicz spaces over quasi-metric measure spaces ⋮ Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation ⋮ Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents

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