Maximal convergence of faber series in weighted smirnov classes with variable exponent on the domains bounded by smooth curves

Abstract

In this paper, we suppose that the boundary of a domain G in the complex plane ℂ belongs to a special subclass of smooth curves and that the canonical domain GR, R > 1 is the largest domain where a function f is analytic. We investigate the rate of convergence to the function f by the partial sums of Faber series of the function f on the domain G. Under the boundary conditions of the domain G, we obtain some results which characterize the maximal convergence of the Faber expansion of the function f which belongs to the weighted Smirnov class with variable exponent [Formula presented].