Approximation in Smirnov classes with variable exponent

Abstract

In this work, the inverse problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on the Jordan domains with a Dini-smooth boundaries, is studied. First, for this purpose, an inverse theorem in the variable exponent Lebesgue spaces of periodic functions is obtained. Later, using the special linear operators, this inverse theorem to the variable exponent Smirnov classes of analytic functions is moved.

Keywords:

• direct theorem
• inverse theorem
• modulus of smoothness
• Faber series
• variable exponent Smirnov classes

AMS Subject Classifications:

• 30E10
• 41A10
• 42A10
• 41A30

Acknowledgements

The authors wish to express deep gratitude to the referees for valuable suggestions.