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Cesàro averaging operators

Published online by Cambridge University Press:  14 November 2011

Krzysztof Stempak
Krzysztof Stempak
Affiliation:
Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
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Abstract

We define a family of Cesàro operators , Reα≧0, and consider the question of their boundedness on Hp spaces. We also consider discrete versions of these operators acting on sequence spaces.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 121 - 126
Copyright
Copyright © Royal Society of Edinburgh 1994

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References

1Brown, A., Halmos, P. R. and Shields, A. L.. Cesàro operators. Acta Sci. Math. 26 (1965), 125–137.Google Scholar
2Cowen, C. C.. Subnormality of the Cesaro operator and a semigroup of composition operators. Indiana Univ. Math. J. 33 (1984), 305–318.CrossRefGoogle Scholar
3Duren, P. L.. Theory of W spaces (New York: Academic Press, 1970).Google Scholar
4Hardy, G. H. and Littlewood, J. E.. Some properties of fractional integrals, II. Math. Z. 34 (1932), 403–439.CrossRefGoogle Scholar
5Miao, J.. The Cesàro operator is bounded on Hp for 0 < p <1. Proc. Amer. Math. Soc. 116 (1992), 1017–1019.Google Scholar
6Siskakis, A. G.. The Cesaro operator is bounded on H1. Proc. Amer. Math. Soc. 110 (1990), 461–462.Google Scholar
7Siskakis, A. G.. Composition semigroups and the Ces<ro operator on Hp. J. London Math. Soc. 36 (1987), 153–164.CrossRefGoogle Scholar
8Zygmund, A.. Trigonometric Series II (London and New York: Cambridge Univ. Press, 1959).Google Scholar