Premium
Regularity and continuity of commutators of the Hardy–Littlewood maximal function
Author(s) -
Liu Feng,
Xue Qingying,
Zhang Pu
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900013
Subject(s) - commutator , mathematics , bounded mean oscillation , sobolev space , hardy space , bounded function , space (punctuation) , pure mathematics , mathematical analysis , maximal function , function (biology) , besov space , measurable function , interpolation space , functional analysis , algebra over a field , linguistics , philosophy , lie conformal algebra , biochemistry , chemistry , evolutionary biology , gene , biology
Let M be the Hardy–Littlewood maximal function and let [ b , M ] be its corresponding commutator. For 1 < p 1 , p 2 , p , q < ∞ and 1 / p = 1 / p 1 + 1 / p 2 , we show that the commutator [ b , M ] is bounded and continuous from Sobolev spaceW s , p 1( R d )to Sobolev spaceW s , p ( R d ) for 0 ≤ s ≤ 1 when b ∈ W s , p 2( R d ) , from Triebel–Lizorkin spaceF s p 1 , q ( R d ) toF s p , q ( R d ) if b ∈ F s p 2 , q ( R d ) and from Besov spaceB s p 1 , q ( R d ) toB s p , q ( R d ) if b ∈ B s p 2 , q ( R d ) and 0 < s < 1 .