Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications

Abstract EN

The embedding theorems in weighted Besov-Lions type spaces Bp,q,γl,s (Ω;E0,E) in which E0,E are two Banach spaces and E0⊂E are studied.

The most regular class of interpolation space Eα between E0 and E is found such that the mixed differential operator Dα is bounded from Bp,q,γl,s (Ω;E0,E) to Bp,q,γs (Ω;Eα) 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.