Fatou-type theorems for general approximate identities
(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:
https://lup.lub.lu.se/record/1247707
- author
- Carlsson, Marcus LU
- organization
- publishing date
- 2008
- 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
- 2016-04-01 14:32:48
- date last changed
- 2022-03-29 21:30:23
@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}}, url = {{http://www.mscand.dk/article.php?id=3091}}, volume = {{102}}, year = {{2008}}, }