Musielak-Orlicz-Sobolev spaces on metric measure spaces

DOI10.1007/s10587-015-0187-0zbMath1363.46027OpenAlexW2203898282MaRDI QIDQ2948001

Tetsu Shimomura, Takao Ohno

Publication date: 29 September 2015

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

Full work available at URL: http://hdl.handle.net/10338.dmlcz/144281

zbMATH Keywords

Sobolev spacecapacitySobolev's inequalityMusielak-Orlicz spacemetric measure spacevolume doublingHajłasz-Sobolev spaceNewton-Sobolev spacevariable order of differentiation

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) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Analysis on metric spaces (30L99)

Related Items (17)

Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Calderón-Zygmund estimates in generalized Orlicz spaces ⋮ Sobolev embeddings for fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces ⋮ New characterizations of Musielak-Orlicz-Sobolev spaces via sharp ball averaging functions ⋮ Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces ⋮ Fuglede's theorem in generalized Orlicz-Sobolev spaces ⋮ Generalized solution of the double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces ⋮ Unnamed Item ⋮ The Riesz potential in generalized Orlicz spaces ⋮ The double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces ⋮ Maximal and Riesz potential operators on Musielak-Orlicz spaces over metric measure spaces ⋮ Hölder regularity of quasiminimizers under generalized growth conditions ⋮ Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces ⋮ Characterizations of even-order Musielak-Orlicz-Sobolev spaces via ball averages and their derivatives ⋮ Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces ⋮ SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES ⋮ Several remarks on Musielak-Orlicz Hardy spaces

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