摘要
The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.
The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.
