Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

FATOU-TYPE THEOREMS FOR GENERAL APPROXIMATE IDENTITIES

MARCUS CARLSSON
Mathematica Scandinavica
Vol. 102, No. 2 (2008), pp. 231-252
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24493590
Page Count: 22
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
FATOU-TYPE THEOREMS FOR GENERAL APPROXIMATE IDENTITIES
Preview not available

Abstract

For functions f ∈ L1(Rn) we consider extensions to Rn × R+ given by convolving f with an approximate identity. For a 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 Sjögren [4], Rönning [2] and Brundin [1].

Page Thumbnails

  • Thumbnail: Page 
[231]
    [231]
  • Thumbnail: Page 
232
    232
  • Thumbnail: Page 
233
    233
  • Thumbnail: Page 
234
    234
  • Thumbnail: Page 
235
    235
  • Thumbnail: Page 
236
    236
  • Thumbnail: Page 
237
    237
  • Thumbnail: Page 
238
    238
  • Thumbnail: Page 
239
    239
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241
  • Thumbnail: Page 
242
    242
  • Thumbnail: Page 
243
    243
  • Thumbnail: Page 
244
    244
  • Thumbnail: Page 
245
    245
  • Thumbnail: Page 
246
    246
  • Thumbnail: Page 
247
    247
  • Thumbnail: Page 
248
    248
  • Thumbnail: Page 
249
    249
  • Thumbnail: Page 
250
    250
  • Thumbnail: Page 
251
    251
  • Thumbnail: Page 
252
    252