Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces

Authors
Bastero, J Milman, M Ruiz, FJ
Citation
J. Bastero et al., Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces, P AM MATH S, 128(1), 2000, pp. 65-74
Citations number
11
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
128
Issue
1
Year of publication
2000
Pages
65 - 74
Database
ISI
SICI code
0002-9939(200001)128:1<65:ROHMFI>2.0.ZU;2-N
Abstract
For the classical Hardy-Littlewood maximal function Mf, a well known and im portant estimate due to Herz and Stein gives the equivalence (Mf)*(t) simil ar to f**(t). In the present note, we study the validity of analogous estim ates for maximal operators of the form [GRAPHICS] where parallel to . parallel to(p,q) denotes the Lorentz space L(p, q)-norm .