Regularity of maximal functions on Hardy–Sobolev spaces

We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces Ḣ1,p(Rd) when p>d/(d+1). This range of exponents is sharp. As a by‐product of the proof, we obtain similar results for the local Hardy–Sobolev spaces ḣ1,p(Rd) in...

Full description

Saved in:
Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2018-12, Vol.50 (6), p.1007-1015
Main Authors: Pérez, Carlos, Picon, Tiago, Saari, Olli, Sousa, Mateus
Format: Article
Language:English
Subjects:
42B25
42B30
42B35
46E35 (primary)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces Ḣ1,p(Rd) when p>d/(d+1). This range of exponents is sharp. As a by‐product of the proof, we obtain similar results for the local Hardy–Sobolev spaces ḣ1,p(Rd) in the same range of exponents.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12195