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A centred norm inequality for singular integral operators

Published online by Cambridge University Press:  24 October 2008

Richard F. Bass
Richard F. Bass
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A.
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Abstract

Let K be a standard singular integral kernel on ℝ satisfying the usual Hölder continuity condition of order δ, and define (where c is chosen so that the integral of w is 1), the mean of g with respect to the measure w(x) dx, and ‖·‖p the Lp norm with respect to w(x) dx. Although the inequality is not true in general, the centred norm inequality does hold for 1 < p < ∞ if α < δ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 369 - 383
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Bass, R. F.. A probabilistic approach to the boundedness of singular integral operators. In Séminaire de Probabilités XXIV, Lecture Notes in Math. vol. 1426 (Springer-Verlag, 1990), pp. 15–40.Google Scholar
[2]Fefferman, C. and Stein, E. M.. Hp spaces of several variables. Acta Math. 129 (1972), 137–193.CrossRefGoogle Scholar
[3]Stein, E. M.. Singular Integrals and Differentiability Properties of Functions (Princeton University Press, 1970).Google Scholar
[4]Torchinsky, A.. Real-variable Methods in Harmonic Analysis (Academic Press, 1986).Google Scholar