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

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

2007-04-30

arxiv.org/abs/0704.3973v1

Mathematics

Functional Analysis

16 pages

Scientific paper

Suppose $\Gamma$ is a Carleson Jordan curve with logarithmic whirl points, $\varrho$ is a Khvedelidze weight, $p:\Gamma\to(1,\infty)$ is a continuous function satisfying $|p(\tau)-p(t)|\le -\mathrm{const}/\log|\tau-t|$ for $|\tau-t|\le 1/2$, and $L^{p(\cdot)}(\Gamma,\varrho)$ 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 $L_N^{p(\cdot)}(\Gamma,\varrho)$.

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