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A T ( b ) type theorem on the weighted Herz‐type Hardy spaces and applications
Author(s) -
Ruan Jianmiao,
Sun Lijing,
Wu Huoxiong,
Yu Xiao
Publication year - 2016
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.201500132
Subject(s) - mathematics , hardy space , type (biology) , bounded function , singular integral operators , singular integral , homogeneous , pure mathematics , cauchy distribution , mathematical analysis , space (punctuation) , operator (biology) , combinatorics , integral equation , ecology , biology , linguistics , philosophy , biochemistry , chemistry , repressor , gene , transcription factor
This paper gives a T ( b ) type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz‐type Hardy spaces into the weighted local Herz‐type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown that neither is a Calderón–Zygmund singular integral operator bounded on the homogeneous local Herz‐type Hardy space, nor bounded on the classical local Hardy space.