Sobolev's theorem for double phase functionals

DOI10.7153/mia-2020-23-02zbMath1453.46021OpenAlexW3005117189MaRDI QIDQ5108653

Tetsu Shimomura, Takao Ohno, Yoshihiro Mizuta

Publication date: 5 May 2020

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-2020-23-02

zbMATH Keywords

continuitymaximal functionsMusielak-Orlicz spacesRiesz potentialsSobolev's theoremfractional maximal functionsdouble phase functionals

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) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (19)

The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth ⋮ Hardy-Sobolev inequalities in the half-space for double phase functionals ⋮ Maximal and Riesz potential operators in double phase Lorentz spaces of variable exponents ⋮ Hardy and Sobolev inequalities for double phase functionals on the unit ball ⋮ Campanato-Morrey spaces for the double phase functionals with variable exponents ⋮ Sobolev and Trudinger inequalities in weighted Morrey spaces for double phase functionals ⋮ Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces ⋮ Integrability for Hardy operators of double phase ⋮ Hardy-Sobolev inequalities for double phase functionals ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents over metric measure spaces ⋮ Boundedness of integral operators of double phase ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ Campanato-Morrey spaces for the double phase functionals ⋮ Continuity of generalized Riesz potentials for double phase functionals ⋮ Hardy-Sobolev inequalities in the unit ball for double phase functionals ⋮ Boundary growth of Sobolev functions of monotone type for double phase functionals ⋮ Sobolev-type inequalities on Musielak-Orlicz-Morrey spaces of an integral form ⋮ Continuity of generalized Riesz potentials for double phase functionals with variable exponents

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