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Approximate identities in variable L p spaces
Author(s) -
CruzUribe D.,
Fiorenza A.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410479
Subject(s) - mathematics , sobolev space , pointwise , variable (mathematics) , norm (philosophy) , laplace's equation , pure mathematics , heat equation , mathematical analysis , convergence (economics) , laplace transform , boundary value problem , economic growth , political science , law , economics
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 [8], Samko [18] and Sharapudinov [19]. 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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)