Approximation by rational functions on doubly connected domains in weighted generalized grand Smirnov classes

A. Testici

doi:10.37863/umzh.v73i7.559

A. Testici Balikesir Univ., Turkey

DOI: https://doi.org/10.37863/umzh.v73i7.559

Keywords: Doubly connected domai, modulus of smoothnes, Faber-Laurent serie, generalized grand Smirnov clas, Carleson curve

Abstract

UDC 517.5

Let $G\subset \mathbb{C}$ be a doubly connected domain bounded by two rectifiable Carleson curves. In this work, we use the higher modulus of smoothness in order to investigate the approximation properties of $(p-\varepsilon)$-Faber–Laurent rational functions in the subclass of weighted generalized grand Smirnov classes ${E}^{p),\theta } ( {G,\omega })$ of analytic functions.

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