MAXIMAL CONVERGENCE OF FABER SERIES IN WEIGHTED SMIRNOV CLASSES WITH VARIABLE EXPONENT ON THE DOMAINS BOUNDED BY SMOOTH CURVES

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 G(R), 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 E-omega(p(.))(GR).