Maximal convergence of faber series in smirnov-orlicz classes

Abstract

It is known that Faber series are used for solving many problems in mechanical science, such as the problems on the stress analysis in the piezoelectric plane and the problems on the analysis of electro-elastic fields and thermo-elastic fields. In this paper, we consider that G is a complex domain bounded by a curve which belongs to a special subclass of smooth curves and the function f is analytic in the canonical domain G(R), R > 1. We research the rate of convergence to the function f by the partial sums of Faber series of the function f on the domain (G) over bar. We obtain results on the maximal convergence of the partial sums of the Faber series of the function f which belongs to the Smirnov-Orlicz class E-M (G(R)), R > 1.