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Littlewood–Paley and Multiplier Theorems on Weighted Spaces over Locally Compact Vilenkin Groups

✍ Scribed by T.S. Quek

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 222 KB
Volume: 210
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5433

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✦ Synopsis

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 condition w ϱ Ž .

p Ž . for g L ⌫ to be a multiplier on the power weighted L G in terms of its ␣ smoothness condition.

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