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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
DOI: https://doi.org/10.1090/S0002-9939-1983-0695267-9
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.


References [Enhancements On Off] (What's this?)

  • [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their uses in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 0447954 (56:6264)
  • [2] J. Daly and K. Phillips, On singular integrals, multipliers, $ {H^p}$, and Fourier series--The local field case (to appear).
  • [3] L. Hörmander, Estimates for translation invariant operators in $ {L^p}$ spaces, Acta Math. 104 (1960), 93-139. MR 0121655 (22:12389)
  • [4] M. Taibleson and G. Weiss, The molecular characterization of Hardy spaces, Astérisque 77 (1980), 67-149. MR 604370 (83g:42012)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695267-9
Keywords: Multipliers, Hardy spaces, Hörmander condition
Article copyright: © Copyright 1983 American Mathematical Society

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