# Approximation by Faber–Laurent Rational Functions in Variable Exponent Morrey Spaces

Approximation by Faber–Laurent Rational Functions in Variable Exponent Morrey Spaces Let G be a finite Jordan domain bounded by a Dini-smooth curve Γ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Gamma$$\end{document} in the complex plane C\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {C}}$$\end{document}. In this work, approximation properties of the Faber–Laurent rational series expansions in variable exponent Morrey spaces Lp(·),λ(·)(Γ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{p(\cdot ),\lambda (\cdot )}(\Gamma )$$\end{document} are studied. Also, direct theorems of approximation theory in variable exponent Morrey–Smirnov classes, defined in domains with a Dini-smooth boundary, are proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Approximation by Faber–Laurent Rational Functions in Variable Exponent Morrey Spaces

, Volume 22 (4) – Dec 1, 2022
15 pages

/lp/springer-journals/approximation-by-faber-laurent-rational-functions-in-variable-exponent-RYyCFlr8Yi
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00427-z
Publisher site
See Article on Publisher Site

### Abstract

Let G be a finite Jordan domain bounded by a Dini-smooth curve Γ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Gamma$$\end{document} in the complex plane C\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {C}}$$\end{document}. In this work, approximation properties of the Faber–Laurent rational series expansions in variable exponent Morrey spaces Lp(·),λ(·)(Γ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{p(\cdot ),\lambda (\cdot )}(\Gamma )$$\end{document} are studied. Also, direct theorems of approximation theory in variable exponent Morrey–Smirnov classes, defined in domains with a Dini-smooth boundary, are proved.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Dec 1, 2022

Keywords: Faber–Laurent rational functions; Conformal mapping; Dini-smooth curve; Variable exponent Morrey spaces; Modulus of smoothness; 30E05; 30E10; 41A10; 41A20; 41A30

### References

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