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Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application
Author(s) -
Lu Shanzhen,
Yang Dachun
Publication year - 1998
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.19981910112
Subject(s) - mathematics , sublinear function , hardy space , pure mathematics , characterization (materials science) , identity (music) , type (biology) , mathematical analysis , ecology , materials science , physics , acoustics , biology , nanotechnology
The authors establish the boundedness of some sublinear operators in weighted Herz spaces on Vilenkin groups under certain weak local hypotheses on the size of these operators at the identity. This class of operators includes most of the important operators in harmonic analysis on Vilenkin groups. The main theorems are best possible under the conditions of the theorems. As applications, the authors establish the Littlewood‐Paley function characterization of some Herz spaces and the relations between Herz spaces and Herz‐type Hardy spaces.