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Trigonometric Multipliers on H2π

Published online by Cambridge University Press:  20 November 2018

J. E. Daly  and
S. Fridli
J. E. Daly
Affiliation:
Department of Mathematics, University of Colorado, Colorado Springs, CO 80933-7150, U.S.A. e-mail: jedaly@math.uccs.edu
S. Fridli
Affiliation:
Department of Numerical Analysis, Eőtvős L. University, Budapest, Pázmány P. sétány, 1\, C, H-1117 Hungary e-mail: fridli@ludens.elte.hu
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Abstract

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In this paper we consider multipliers on the real Hardy space ${{H}_{2\pi }}$. It is known that the Marcinkiewicz and the Hörmander–Mihlin conditions are sufficient for the corresponding trigonometric multiplier to be bounded on $L_{2\pi }^{p},1<p<\infty$. We show among others that the Hörmander– Mihlin condition extends to ${{H}_{2\pi }}$ but the Marcinkiewicz condition does not.

Keywords

42A45;42A5042A85MultipliersHardy space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 370 - 381
Copyright
Copyright © Canadian Mathematical Society 2005

References

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