Approximate identities in variable L p spaces |
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| Authors: | D Cruz‐Uribe SFO A Fiorenza |
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| Institution: | 1. Department of Mathematics, Trinity College, Hartford, CT 06106‐3100, USAPhone: +1 860 297 2297, Fax: +1 860 987 6239;2. Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universitá di Napoli, Via Monteoliveto, 3, I–80134 Napoli, Italy;3. Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sezione di Napoli, Consiglio Nazionale delle Ricerche, Via Pietro Castellino, 111, I–80131 Napoli, Italy;4. Phone: +39 081 2538912, Fax: +39 081 2538909 |
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| 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) |
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| Keywords: | Variable Sobolev space variable Lebesgue space approximate identities |
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