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arXiv · 0704.3973

Semi-Fredholm singular integral operators with piecewise continuous coefficients on weighted variable Lebesgue spaces are Fredholm

Alexei Yu. Karlovich
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Abstract

Suppose $Γ$ is a Carleson Jordan curve with logarithmic whirl points, $\varrho$ is a Khvedelidze weight, $p:Γ\to(1,\infty)$ is a continuous function satisfying $|p(τ)-p(t)|\le -\mathrm{const}/\log|τ-t|$ for $|τ-t|\le 1/2$, and $L^{p(\cdot)}(Γ,\varrho)$ is a weighted generalized Lebesgue space with variable exponent. We prove that all semi-Fredholm operators in the algebra of singular integral operators with $N\times N$ matrix piecewise continuous coefficients are Fredholm on $L_N^{p(\cdot)}(Γ,\varrho)$.

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Alexei Yu. Karlovich. 2007-04-30. Semi-Fredholm singular integral operators with piecewise continuous coefficients on weighted variable Lebesgue spaces are Fredholm. https://arxiv.org/abs/0704.3973

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