Let be homogeneous of degree 0 in and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor in the denition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels , provided that the mean value of 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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Peter Sjögren, Fernando Soria, Rough maximal functions and rough singular integral operators applied to integrable radial functions. Rev. Mat. Iberoam. 13 (1997), no. 1, pp. 1–18DOI 10.4171/RMI/216