Revista Matemática Iberoamericana


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Volume 13, Issue 1, 1997, pp. 1–18
DOI: 10.4171/RMI/216

Published online: 1997-04-30

Rough maximal functions and rough singular integral operators applied to integrable radial functions

Peter Sjögren[1] and Fernando Soria[2]

(1) Chalmers University of Technology, Göteborg, Sweden
(2) Universidad Autónoma de Madrid, Spain

Let $\Omega$ be homogeneous of degree 0 in $\mathbb R^n$ and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor $\Omega$ in the denition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels $\Omega(y)/|y|^n$, provided that the mean value of $\Omega$ vanishes. In an earlier paper, the authors showed that a two-dimensional rough maximal operator is of weak type (1,1) when restricted to radial functions. This result is now extended to arbitrary finite dimension, and to rough singular integrals.

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Sjögren Peter, Soria Fernando: Rough maximal functions and rough singular integral operators applied to integrable radial functions. Rev. Mat. Iberoam. 13 (1997), 1-18. doi: 10.4171/RMI/216