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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

[DF] Daly, J. and Fridli, S., Walsh multipliers for dyadic Hardy spaces. Appl. Anal. 82(2003), 689–700.Google Scholar
[EG] Edwards, R. E. and Gaudry, G. I., Littlewood-Paley and multiplier theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 90. Springer-Verlag, Berlin, 1977.Google Scholar
[H] Hörmander, L., Estimates for translation invariant operators in Lp spaces. Acta Math. 104(1960), 93–140.Google Scholar
[Ki] Kislyakov, S. V., Classical themes of Fourier analylsis. Commutative harmonic analysis, I, Encyclopaedia Math. Sci. 15, Springer, Berlin, 1991, 113–165.Google Scholar
[Ma] Marcinkiewicz, J., Sur les multiplicateurs des séries de Fourier. Studia Math. 8(1939), 78–91.Google Scholar
[Mi] Mihlin, S. G., On the multipliers of Fourier integrals. Dokl. Akad. Nauk SSSR, 109(1956), 701–703.(Russian).Google Scholar
[Mó] Móricz, F., Sidon type inequalities. Publ. Inst. Math.(Beograd) (N.S.) 48(1990), 101–109.Google Scholar
[Sch] Schipp, F., Sidon-type inequalities. Lecture Notes in Pure and Appl. Math. 138, Dekker, New York, 1992, pp. 421–436.Google Scholar
[Zy] Zygmund, A., Trigonometric Series. 2nd ed. Cambridge University Press, New York, 1959.Google Scholar