Approximate identities in variable Lp spaces
David V. Cruz-Uribe, Alberto Fıorenza · Mathematische Nachrichten · 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 [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)