El-Shobaky, E. M.; Abdel-Mottaleb, N.; Fathi, A.; Faragallah, M. Interpolation methods to estimate eigenvalue distribution of some integral operators. (English) Zbl 1092.47030 Int. J. Math. Math. Sci. 2004, No. 9-12, 479-485 (2004). 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. Reviewer: Birgit Jacob (Delft) MSC: 47B34 Kernel operators 47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators Keywords:eigenvalue distribution; integral operators; Triebel-Lizorkin function space PDFBibTeX XMLCite \textit{E. M. El-Shobaky} et al., Int. J. Math. Math. Sci. 2004, No. 9--12, 479--485 (2004; Zbl 1092.47030) Full Text: DOI EuDML