Rough maximal functions and rough singular integral operators applied to integrable radial functions
Peter Sjögren, Fernando Soria · Revista Matemática Iberoamericana · 1997
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.