Shakhmurov, Veli2024-05-252024-05-2520122090-89970972-680210.1155/2012/8193212-s2.0-84864925272https://doi.org/10.1155/2012/819321https://hdl.handle.net/20.500.14517/588The embedding theorems in weighted Besov-Lions type spaces B-p,q,gamma(l,s) (Omega; E-0, E) in which E-0, E are two Banach spaces and E-0 subset of E are studied. The most regular class of interpolation space E-alpha between E-0 and E is found such that the mixed differential operator D-alpha is bounded from B-p,q,gamma(l,s) (Omega; E-0, E) to B-p,q,gamma(s) (Omega; E-alpha) and Ehrling-Nirenberg-Gagliardo type sharp estimates are established. By using these results, the uniform separability of degenerate abstract differential equations with parameters and the maximal B-regularity of Cauchy problem for abstract parabolic equations are obtained. The infinite systems of the degenerate partial differential equations and Cauchy problem for system of parabolic equations are further studied in applications.eninfo:eu-repo/semantics/openAccess[No Keyword Available]Article1