International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 9, Pages 479-485

Interpolation methods to estimate eigenvalue distribution of some integral operators

E. M. El-Shobaky,1 N. Abdel-Mottaleb,1 A. Fathi,1 and M. Faragallah2

1Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
2Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt

Received 20 August 2002

Copyright © 2004 E. M. El-Shobaky et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the asymptotic distribution of eigenvalues of integral operators Tk defined by kernels k which belong to Triebel-Lizorkin function space Fpuσ(Fqvτ) by using the factorization theorem and the Weyl numbers xn. We use the relation between Triebel-Lizorkin space Fpuσ(Ω) and Besov space Bpqτ(Ω) and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizorkin spaces Fpuσ(Fqvτ).