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On the convergence of certain singular integrals

Published online by Cambridge University Press:  24 October 2008

K. J. Falconer
K. J. Falconer
Affiliation:
University of Bristol
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Extract

Hardy (3) provides one of the earliest rigorous discussions of the convergence of Riemann multiple integrals of real functions with a general type of algebraic singularity. More recently, and with the advent of Lebesgue integration, various authors such as Garsia(2) have investigated singular integrals involving more general measurable functions. In this paper we shall develop an indirect potential theoretic method to obtain convergence criteria for a class of multiple integral that seems to have been neglected to date.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 3 , May 1981 , pp. 397 - 403
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Carleson, L.Selected problems on exceptional sets (Van Nostrand, Princeton, 1967).Google Scholar
(2)Garsia, A. M.Combinatorial inequalities and smoothness of functions. Bull. Amer. Math. Soc. 82 (1976), 157–170.CrossRefGoogle Scholar
(3)Hardy, G. H.Notes on some points in the integral calculus. Messenger of Math. 31 (1902), 125–128.Google Scholar
(4)Herz, C. S.Fourier transforms related to convex sets. Ann. of Math. 75 (1962), 81–92.CrossRefGoogle Scholar
(5)Littman, W.Fourier transforms of surface carried measures and differentiability of surface averages. Bull. Amer. Math. Soc. 69 (1963), 766–770.CrossRefGoogle Scholar