Sobolev and Trudinger type inequalities on grand Musielak-Orlicz-Morrey spaces. (English) Zbl 1327.31017
The authors define the (generalized) grand Musielak-Orlicz-Morrey space on a bounded open set of \({\mathbb R}^N\) on which Sobolev and Trudinger type inequalities are obtained for general potentials of functions.
Reviewer: Marius Ghergu (Dublin)
MSC:
| 31B15 | Potentials and capacities, extremal length and related notions in higher dimensions |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
grand Musielak-Orlicz-Morrey spaces; Riesz potentials; maximal functions; Sobolev’s inequality; Trudinger’s inequalityReferences:
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