Premium
Chanillo–Wheeden Inequalities for 0 < p ⩽ 1
Author(s) -
Wilson J. Michael
Publication year - 1990
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-41.2.283
Subject(s) - combinatorics , mathematics , maximal operator , function (biology) , maximal function , operator (biology) , mathematical analysis , chemistry , biochemistry , repressor , evolutionary biology , gene , transcription factor , bounded function , biology
For f ∈ S , a tempered distribution, let S ( f ) be a real‐variable variant of the Lusin area function of f and let G ( f ) be the Fefferman–Stein ‘grand’ maximal function of f . Let M denote the usual Hardy–Littlewood maximal operator. We prove that for all 0 < p ⩽ 1 there is a C ( p, d ) < ∞ such that∫ S p ( f ) V d x ⩽ C ( p , d ) ∫| G ( f ) | p M V d xfor all f and for all non‐negative weights V .