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The embedding theorems in anisotropic Besov-Lions type spaces Open image in new window  are studied; here Open image in new window  and Open image in new window  are two Banach spaces. The most regular spaces Open image in new window  are found such that the mixed differential operators Open image in new window  are bounded from Open image in new window  to Open image in new window , where Open image in new window  are interpolation spaces between Open image in new window  and Open image in new window  depending on Open image in new window  and Open image in new window . By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal Open image in new window -regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.

Embedding theorems in Banach-valued B-spaces and maximal B-regular differential-operator equations