Maximal Convergence by Faber Series in Morrey-Smirnov Classes with Variable Exponents

Abstract

In this paper, we assume that G is a domain bounded by ? Dini-smooth curve and R > 1 is the largest number such that a function f is analytic inside the level curve ?R in the exterior of ?. By taking the function f in the Morrey- Smirnov classes with variable exponents Ep(·), ?(·)(GR), we obtain a rate of maximal convergence of the nth partial sums of the Faber series of the function f in the uniform norm on the closure of G. Here the rate of maximal convergence depends on the best approximation number Ep(·), ?(·)n(f, GR). © 2024 Burcin Oktay.