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

Veli B. Shakhmurov

 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

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.