Revista Matemática Iberoamericana
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Published online: 1997-04-30
Rough maximal functions and rough singular integral operators applied to integrable radial functionsPeter Sjögren and Fernando Soria (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