Resumen de Rough maximal functions and rough singular integral operators applied to integrable radical functions

Fernando Soria de Diego , Peter Sjögren

• Let O be homogeneous of degree 0 in Rn and integrable on the unit sphere. A rough maximal operator is obtained by inserting a factor O in the definition of the ordinary maximal function. Rough singular integral operators are given by principal value kernels O(y) / |y|n, provided that the mean value of O 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.