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Fatou-type theorems for general approximate identities

På svenska

Author

Summary, in English

For functions. f is an element of L-1 (R-n) we consider extensions to R-n x R+ given by convolving f with an approximate identity. Fora large class of approximate identities we obtain a Fatou-type theorem where the convergence regions are sometimes effectively larger than the non-tangential ones. We then study a more restricted class of approximate identities for which the convergence regions are shown to be optimal. Finally we will consider products of approximate identities. The results extend previous results by Sjogren [4], Ronning [2] and Brundin [1].

Publishing year

2008

Language

English

Pages

231-252

Publication/Series

Mathematica Scandinavica

Volume

102

Issue

2

Document type

Journal article

Publisher

Matematisk Institut

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 0025-5521