Shakhmurov, Veli2024-05-252024-05-25201110252-96021572-908710.1016/S0252-9602(11)60207-52-s2.0-78650976523https://doi.org/10.1016/S0252-9602(11)60207-5https://hdl.handle.net/20.500.14517/565The weighted Sobolev-Lions type spaces W-p,gamma(l) (Omega; E) boolean AND L-p,L-gamma (Omega; E-0) are studied, where E-0, E are two Banach spaces and E-0 is continuously and densely embedded on E. A new concept of capacity of region Omega is an element of R-n in Wp,gamma(l)(Omega; E-0, E) is introduced. Several conditions in terms of capacity of region Omega and interpolations of E-0 and E are found such that ensure the continuity and compactness of embedding operators. In, particular, the most regular class of interpolation spaces E-alpha between E-0 and E, depending of alpha and l, are found such that mixed differential operators D-alpha are bounded and compact from W-p,gamma(l)(Omega; E-0, E) to E-alpha-valued L-p,L-gamma spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.eninfo:eu-repo/semantics/closedAccessCapacity of regionsembedding theoremsBanach-valued function spacesdifferential-operator equationsSemigroups of operatorsoperator-valued Fourier multipliersinterpolation of Banach spacesArticleQ2Q33114967WOS:000287165300007