NONLINEAR m-SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENC

Abstract

In the present paper, we prove some theorems concerning Fatou type weighted pointwise convergence of nonlinear msingular integral operators of the form: T [m] (f; x) = Z R K t;Xm k=1 (1)k1 m k f(x + kt) ! dt; where x 2 R; m 1 is a Önite natural number and 2 which is a nonempty set of non-negative indices, at a common m p Lebesgue point of f 2 Lp;'(R) (1 p < 1) and ': Here, ' : R ! R+ is a weight function endowed with some speciÖc properties and Lp;'(R) is the space of all measurable functions for which rable functions for which f ' p is integrabl on R.