Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\)
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Publication:930977
DOI10.1016/j.jmaa.2008.03.067zbMath1153.31002OpenAlexW1983925403MaRDI QIDQ930977
Yoshihiro Mizuta, Tetsu Shimomura, Takao Ohno
Publication date: 24 June 2008
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.03.067
Related Items (32)
Embedding operators of Sobolev spaces with variable exponents and applications ⋮ Compact embeddings for Sobolev spaces of two variable exponents ⋮ Generalized Orlicz spaces and related PDE ⋮ Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials ⋮ Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent ⋮ A trace inequality of Riesz potentials in variable exponent Orlicz spaces ⋮ Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \(\mathbb{R}^n\) ⋮ Exponential integrability of Riesz potentials of Orlicz functions ⋮ Musielak-Orlicz-Sobolev spaces on metric measure spaces ⋮ Sobolev's inequality for double phase functionals with variable exponents ⋮ Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth ⋮ Sobolev inequalities for Musielak-Orlicz spaces ⋮ Characterization of generalized Orlicz spaces ⋮ On the boundary limits of monotone Sobolev functions in variable exponent Orlicz spaces ⋮ Iterated maximal functions in variable exponent Lebesgue spaces ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ Capacity for potentials of functions in Musielak-Orlicz spaces ⋮ The Riesz potential in generalized Orlicz spaces ⋮ Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces ⋮ Growth properties of Musielak-Orlicz integral means for Riesz potentials ⋮ Fractional integrals over a function of finite type on the intersection spaces ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ Weighted Sobolev inequality in Musielak-Orlicz space ⋮ Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces ⋮ SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS ⋮ Maximal and Riesz potential operators on Musielak-Orlicz spaces over metric measure spaces ⋮ Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent ⋮ Boundary limits of monotone Sobolev functions with variable exponent on uniform domains in a metric space ⋮ Potential operators and their commutators acting between variable Lebesgue spaces with different weights ⋮ Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian ⋮ Compact embeddings in the generalized Sobolev space \(W_0^{1,p(\cdot)}(G)\) and existence of solutions for nonlinear elliptic problems ⋮ Sobolev-type inequalities on Musielak-Orlicz-Morrey spaces of an integral form
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