Algebras of singular integral operators on Nakano spaces with Khvedelidze weights over Carleson curves with logarithmic whirl points

TL;DR

This paper develops a Fredholm criterion for singular integral operators with piecewise continuous coefficients on Nakano spaces equipped with Khvedelidze weights over Carleson curves featuring logarithmic whirl points, advancing operator theory in variable exponent spaces.

Contribution

It introduces a new Fredholm criterion for singular integral operators on Nakano spaces with complex weights over intricate curves, expanding the theoretical framework in variable exponent analysis.

Findings

Established a Fredholm criterion for operators on Nakano spaces

Analyzed operators over Carleson curves with logarithmic whirl points

Extended operator theory to weighted variable exponent spaces

Abstract

We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze weights over Carleson curves with logarithmic whirl points.