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Interpolation methods to estimate eigenvalue distribution of some integral operators. (English) Zbl 1092.47030

In this paper, integral operators with kernels belonging to the Triebel-Lizorkin function space \(F_{pu}^\sigma(\Omega;(F^\tau_{qv};\Omega))\) are studied. Here, \(\Omega\) is a bounded domain in \(\mathbb R^N\). The main theorem says that the eigenvalues of these integral operators belong to the Lorenz sequence space \(\ell_{r,p}\), where \(r\) depends on \(\sigma\), \(\tau\), \(N\) and \(q\). For the proof of this result, the authors use the relation between Triebel-Lizorkin spaces and Besov spaces, and an interpolation method.

MSC:

47B34 Kernel operators
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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