THE HARDY-LITTLEWOOD MAXIMAL-FUNCTION OF A SOBOLEV FUNCTION

Authors
KINNUNEN J
Citation
J. Kinnunen, THE HARDY-LITTLEWOOD MAXIMAL-FUNCTION OF A SOBOLEV FUNCTION, Israel Journal of Mathematics, 100, 1997, pp. 117-124
Citations number
5
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Israel Journal of Mathematics → ACNP
ISSN journal
00212172
Volume
100
Year of publication
1997
Pages
117 - 124
Database
ISI
SICI code
0021-2172(1997)100:<117:THMOAS>2.0.ZU;2-L
Abstract
We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev space W-1,W-p(R-n) for 1 < p less than or equal to infinity. A s an application we study a weak type inequality for the Sobolev capac ity. We also prove that the Hardy-Littlewood maximal function of a Sob olev function is quasi-continuous.