Fatou type weighted pointwise convergence of nonlinear singular integral operators Depending on two parameters
Serenbay, Sevilay Kirci
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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.