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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695267-9
PII: S 0002-9939(1983)0695267-9
Keywords: Multipliers, Hardy spaces, Hörmander condition
Article copyright: © Copyright 1983 American Mathematical Society