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

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Abstract

Let G be a finite Jordan domain bounded by a Dini-smooth curve \(\Gamma \) in the complex plane \({\mathbb {C}}\). In this work, approximation properties of the Faber–Laurent rational series expansions in variable exponent Morrey spaces \(L^{p(\cdot ),\lambda (\cdot )}(\Gamma )\) are studied. Also, direct theorems of approximation theory in variable exponent Morrey–Smirnov classes, defined in domains with a Dini-smooth boundary, are proved.

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Acknowledgements

The author would like to thank the referees for all their valuable advice and helpful remarks.

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Authors and Affiliations

  1. Department of Mathematics and Science Education, Faculty of Education, Muş Alparslan University, 49250, Muş, Turkey

    Sadulla Z. Jafarov

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 9 B. Vahabzadeh Str., 1141, Baku, Azerbaijan

    Sadulla Z. Jafarov

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Correspondence to Sadulla Z. Jafarov.

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Communicated by Vladimir V. Andrievskii.

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Jafarov, S.Z. Approximation by Faber–Laurent Rational Functions in Variable Exponent Morrey Spaces. Comput. Methods Funct. Theory 22, 629–643 (2022). https://doi.org/10.1007/s40315-021-00427-z

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