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Pointwise convergence of spherical means

Published online by Cambridge University Press:  24 October 2008

Andreas Seeger ,
Stephen Wainger  and
James Wright
Andreas Seeger
Affiliation:
University of Wisconsin, Madison, WI 53706, U.S.A.
Stephen Wainger
Affiliation:
University of Wisconsin, Madison, WI 53706, U.S.A.
James Wright
Affiliation:
University of Sussex, Falmer, Brighton BN1 9QH
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Extract

For a function f ∈ Lp(ℝd) we define the spherical means

where dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. We consider the problem of pointwise convergence of the means , for any particular sequence tj → 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 115 - 124
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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