Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: EMBEDDING THEOREMS IN BANACH-VALUED B-SPACES AND MAXIMAL B-REGULAR DIFFERENTIAL-OPERATOR EQUATIONS | EMBEDDING THEOREMS IN BANACH-VALUED B-SPACES AND MAXIMAL B-REGULAR DIFFERENTIAL-OPERATOR EQUATIONS VELI B. SHAKHMUROV Received 28 September 2004 Revised 8 November 2005 Accepted 4 May 2006 The embedding theorems in anisotropic Besov-Lions type spaces Blp g Rn E0 E are studied here E0 and E are two Banach spaces. The most regular spaces Ea are found such that the mixed differential operators Da are bounded from Blp g Rn E0 E to BSq g Rn Ea where Ea are interpolation spaces between E0 and E depending on a a1 a2 . an and l 11 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. 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. Introduction Embedding theorems in function spaces have been studied in 8 35 37 38 . A comprehensive introduction to the theory of embedding of function spaces and historical references may be also found in 37 . In abstract function spaces embedding theorems have been investigated in 4 5 10 17 21 27 34 40 . Lions and Peetre 21 showed that if u e L2 0 T H0 u m e L2 0 T H then u i e L2 0 T H Hi i m i 1 2 . m 1 where H0 H are Hilbert spaces H0 is continuously and densely embedded in H where H0 H g are interpolation spaces between H0 and H for 0 g 1. The similar questions for anisotropic Sobolev spaces wlp Q H0 H Q c Rn and for corresponding weighted Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2006 Article ID 16192 Pages 1-22 DOI JIA 2006 16192 2 Embedding and B-regular operators spaces have been investigated in
