Abstract
This study focuses on the anisotropic Besov-Lions type spaces Bp,θl(Ω;E0,E) associated with Banach spaces E0 and E. Under certain conditions, depending on l = (l1, l2,⋯, ln) and α = (α1, α2, ⋯, αn), the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators Dα are bounded and compact from Bp,θl+s(Ω;E0,E) to Bp,θs(Ω;Eα). These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties.
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