Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 16192, 22 pages
doi:10.1155/JIA/2006/16192
Embedding theorems in Banach-valued B-spaces and maximal B-regular differential-operator equations
Department of Electrical & Electronics Engineering, Engineering Faculty, Istanbul University, Istanbul 34320, Avcilar, Turkey
Received 28 September 2004; Revised 8 November 2005; Accepted 4 May 2006
Copyright © 2006 Veli B. Shakhmurov. 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.
Abstract
The embedding theorems in anisotropic Besov-Lions type spaces Bp,θl(Rn;E0,E) are studied; here E0 and E are two Banach spaces. The most regular spaces Eα are found such that the mixed differential operators Dα are bounded from Bp,θl(Rn;E0,E) to Bq,θs(Rn;Eα), where Eα are interpolation spaces between E0 and E depending on α=(α1,α2,⋯,αn) and l=(l1,l2,⋯,ln). By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal B-regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.