WEIGHTED Lp BOUNDEDNESS OF CARLESON TYPE MAXIMAL OPERATORS.

In 2001, E. M. Stein and S. Wainger gave the Lp boundedness of the Carleson type maximal operator Τ*, which is defined by Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. In this paper, the authors show that if K is a homogeneous kernel, i.e. K(y) = Ω(y!)|y|--n, then Stein-Wainger's result still holds on the weighted Lp spaces when Ω satisfies only an Lq-Dini condition for some 1 < q ≤ ∞. [ABSTRACT FROM AUTHOR]