The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces

Alexei Yu. Karlovich, Ilya M. Spitkovsky

Let $p:\mathbb{R}\to (1,\infty )$ be a globally log-Hölder continuous variable exponent and $w:\mathbb{R}\to [0,\infty ]$ be a weight. We prove that the Cauchy singular integral operator $S$ is bounde…