On the necessity of the Hörmander condition for multipliers on $\textbf {H}^{p}(\textbf {R}^{n})$
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- by James E. Daly PDF
- Proc. Amer. Math. Soc. 88 (1983), 321-325 Request permission
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
- Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5 J. Daly and K. Phillips, On singular integrals, multipliers, ${H^p}$, and Fourier series—The local field case (to appear).
- Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
- Mitchell H. Taibleson and Guido Weiss, The molecular characterization of certain Hardy spaces, Representation theorems for Hardy spaces, Astérisque, vol. 77, Soc. Math. France, Paris, 1980, pp. 67–149. MR 604370
Additional Information
- © Copyright 1983 American Mathematical Society
- 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