Interpolation methods to estimate eigenvalue distribution of some integral operators
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.
scientific article; zbMATH DE number 2168627