We extend the Littlewood᎐Paley theorem to L G , where G is a locally w compact Vilenkin group and w are weights satisfying the Muckenhoupt A p condition. As an application we obtain a mixed-norm type multiplier result on p Ž . L G and prove the sharpness of our result. We also obtain a sufficient co
Littlewood–Paley and Pseudo-Differential Operators on Herz-type Spaces over Vilenkin Groups
✍ Scribed by Yue Ping Zhu
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2004
- Tongue
- English
- Weight
- 155 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1439-7617
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📜 SIMILAR VOLUMES
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. T
## Abstract Let __G__ be a locally compact Vilenkin group. Using Herz spaces, we give sufficient conditions for a distribution on __G__ to be a convolution operator on certain Lorentz spaces. Our results generalize Hörmander's multiplier theorem on __G__. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, W