Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the necessity of the Hörmander condition for multipliers on $ {\bf H}\sp{p}({\bf R}\sp{n})$

Author: James E. Daly
Journal: Proc. Amer. Math. Soc. 88 (1983), 321-325
MSC: Primary 42B30
MathSciNet review: 695267
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Abstract: In this paper we prove that a class of multiplier operators on $ {{\mathbf{H}}^p}({{\mathbf{R}}^n})$, that send atoms to molecules boundedly, must satisfy a Hörmander condition. This provides a partial converse to a theorem of Taibleson and Weiss.

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Keywords: Multipliers, Hardy spaces, Hörmander condition
Article copyright: © Copyright 1983 American Mathematical Society