Fatou type weighted pointwise convergence of nonlinear singular integral operators Depending on two parameters

Abstract

In this paper we present some theorems concerning existence and Fatou type weighted pointwise convergence of nonlinear singular integral operators of the form:

(T(lambda)f)(x) =integral K-R(lambda)(t-x; f(t))dt, x is an element of R, lambda is an element of Lambda

where Lambda not equal empty set is a set of non-negative indices, at a common generalized Lebesgue point of the functions f is an element of L-1,L-empty set (R) and positive weight function empty set. Here, L-1,L-empty set(R) is the space of all measurable functions for which vertical bar f/empty set vertical bar is integrable on R.