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Fourier operators on weighted Hardy spaces

Published online by Cambridge University Press:  24 October 2008

Hans P. Heinig
Hans P. Heinig
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ont. L8S4K1, Canada
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Abstract

In this note we utilize the atomic decomposition of weighted Hardy spaces to prove weighted versions of Hardy's inequality for the Fourier transform with Muckenhoupt weight. The result extends to certain integral operators with homogeneous kernels of degree −1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 113 - 121
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

[1]Andersen, K. F. and Heinig., H. P.Weighted norm inequalities for certain integral operators. SIAM J. Math. Anal. 14, 4 (1983), 834–844.CrossRefGoogle Scholar
[2]Benedetto, J. J., Heinig, H. P. and Johnson., R.Weighted Hardy spaces and the Laplace transform II. Math. Nachrichten (to appear).Google Scholar
[3]Coifman, R. R. and Weiss., G.Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569–645.CrossRefGoogle Scholar
[4]Duren., P. L.Theory of Hv-spaces (Academic Press, 1970).Google Scholar
[5]Garcia-Cuerva., J.Weighted Hp-spaces. Diasertationes Math, CLXII, (1979), 1–63.Google Scholar
[6]Hardy, G. H. and Littlewood., J. E.Some new properties of Fourier constants. Math. Ann. 97 (1926), 159–209.CrossRefGoogle Scholar
[7]Heinig., H. P.Weighted norm inequalities for classes of operators. Indiana Univ. Math. J. 33 (1984), 573–582.CrossRefGoogle Scholar
[8]Hunt, R., Muckenhoupt, B. and Wheeden., R.Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc. 176 (1973), 227–251.CrossRefGoogle Scholar
[9]Jodeit, M. Jr and Shaw., K. K. Hardy kernels and H 1(R) (preprint).Google Scholar
[10]Muckenhoupt., B.Weighted norm inequalities for the Fourier transform. Trans. Amer. Math. Soc. 176 (1983), 729–742.CrossRefGoogle Scholar
[11]Muckenhoupt., B.Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226.CrossRefGoogle Scholar