International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 9, Pages 479-485
doi:10.1155/S0161171204208274

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

Abstract

We study the asymptotic distribution of eigenvalues of integral operators Tk defined by kernels k which belong to Triebel-Lizorkin function space Fpuσ(F  qvτ) 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(F  qvτ).