EMBEDDING THEOREMS IN BANACH-VALUED B-SPACES AND MAXIMAL B-REGULAR DIFFERENTIAL-OPERATOR EQUATIONS

The embedding theorems in anisotropic Besov-Lions type spaces Blp,θ(R n;E0,E) are stud-ied; 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 Blp,θ(R n;E0,E) to Bsq,θ(R n;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 stud-ied. 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. 1