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Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

✍ Scribed by Shanzhen Lu; Dachun Yang

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
708 KB
Volume
191
Category
Article
ISSN
0025-584X

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✦ Synopsis

The authors establish the boundedness of some sublinear operators in weighted Herr 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 Herr spaces and the relations between Hers spaces and Herz -type Hardy spaces.

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