Approximation by p-Faber-Laurent rational functions in the weighted Lebesgue spaces

Abstract

Let L subset of C be a regular Jordan curve. In this work, the approximation properties of the p-Faber-Laurent rational series expansions in the w weighted Lebesgue spaces L-p(L, w) are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a kth integral modulus of continuity in L-p (L, w) spaces is estimated.