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Fatou-type theorems for general approximate identities

Carlsson, Marcus LU (2008) In Mathematica Scandinavica 102(2). p.231-252
Abstract
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].
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematica Scandinavica
volume
102
issue
2
pages
231 - 252
publisher
Matematisk Institut
external identifiers
  • wos:000258857100003
  • scopus:49349109803
ISSN
0025-5521
language
English
LU publication?
yes
id
415108f5-4f8b-4b6c-bb27-b060eae88b18 (old id 1247707)
alternative location
http://www.mscand.dk/article.php?id=3091
date added to LUP
2008-11-10 12:21:45
date last changed
2017-01-01 06:17:54
@article{415108f5-4f8b-4b6c-bb27-b060eae88b18,
  abstract     = {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].},
  author       = {Carlsson, Marcus},
  issn         = {0025-5521},
  language     = {eng},
  number       = {2},
  pages        = {231--252},
  publisher    = {Matematisk Institut},
  series       = {Mathematica Scandinavica},
  title        = {Fatou-type theorems for general approximate identities},
  volume       = {102},
  year         = {2008},
}