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Growth of functions in Hp

Published online by Cambridge University Press:  17 April 2009

Hwai-Chiuan Wang
Hwai-Chiuan Wang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China.
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Abstract

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There are two Hardy and Littlewood theorems which describe the rate of growth of functions in Hp on the unit circle T. In this paper we first establish their analogues on Euclidean space Rn and then apply them to solve multiplier and factorization problems on Hp(Rn).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 147 - 156
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Coifman, Ronald R., “A real variable characterization of Hp”, Studia Math. 51 (1974), 269–274.Google Scholar
[2]Coifman, Ronald R. and Weiss, Guido, “Extensions of Hardy space and their use in analysis”, Bull. Amer. Math. Soc. 83 (1977), 569–645.Google Scholar
[3]Fefferman, Charles, “Characterizations of bounded mean oscillation”, Bull. Amer. Math. Soc. 77 (1971), 587–588.Google Scholar
[4]Fefferman, C. and Stein, E.M., “Hp spaces of several variables”, Acta Math. 129 (1972), 137–193.Google Scholar
[5]Feichtinger, Hans G., Graham, Colin C. and Lakien, Eric H., “Nonfactorization in commutative, weakly self-adjoint Banach algebras”, Pacific J. Math. 80 (1979), 117–125.CrossRefGoogle Scholar
[6]Hardy, G.H. und Littlewood, J.E., “Some new properties of Fourier constants”, Math. Ann. 97 (1927), 159–209.Google Scholar
[7]Hardy, G.H. and Littlewood, J.E., “Some properties of fractional integrals. II”, Math. Z. 34 (1932), 403–439.Google Scholar
[8]Latter, Robert H., “A characterization of Hp(Rn) in terms of atoms”, Studia Math. 62 (1977), 93–101.Google Scholar
[9]Neri, Umberto, “Fractional integration on the space H 1 and its dual”, Studia Math. 53 (1975), 175–189.Google Scholar
[10]Peetre, Jaak, “Two observations on a theorem by Coifman”, Studia Math. 64 (1979), 191–194.Google Scholar
[11]Wang, Hwai-chiuan, “A note on Segal algebras on Euclidean spaces”, Proc. Amer. Math. Soc. 77 (1978), 513–518.Google Scholar
[12]Wang, Hwai-Chiuan, Homogeneous Banach algebras (Lecture Notes in Pure and Applied Mathematics, 29. Marcel Dekker, New York, Basel, 1977).Google Scholar
[13]Wigley, Neil M., “A Banach algebra structure for Hp”, Canad. Math. Bull. 18 (1975), 597–603.CrossRefGoogle Scholar