We give conditions for the convergence of approximate identities, both pointwise and in norm, in variable $L^p$ spaces. We unify and extend results due to Diening, Samko and Sharapudinov. As applications, we give criteria for smooth functions to be dense in the variable Sobolev spaces, and we give solutions of the Laplace equation and the heat equation with boundary values in the variable $L^p$ spaces.
Approximate identities in variable $L^p$ spaces / D., CRUZ URIBE; Fiorenza, Alberto. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 280:3(2007), pp. 256-270. [DOI 10.1002/mana.200410479]
Approximate identities in variable $L^p$ spaces
FIORENZA, ALBERTO
2007
Abstract
We give conditions for the convergence of approximate identities, both pointwise and in norm, in variable $L^p$ spaces. We unify and extend results due to Diening, Samko and Sharapudinov. As applications, we give criteria for smooth functions to be dense in the variable Sobolev spaces, and we give solutions of the Laplace equation and the heat equation with boundary values in the variable $L^p$ spaces.File in questo prodotto:
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