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 Γ Dini-smooth curve and R > 1 is the largest number such that a function f is analytic inside the level curve Γ_R in the exterior of Γ. By taking the function f in the Morrey-Smirnov classes with variable exponents , 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 .