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| Embedding Theorems in B-Spaces and Applications |
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Citation： |
Veli B. SHAKHMUROV.Embedding Theorems in B-Spaces and Applications[J].Chinese Annals of Mathematics B,2008,29(1):95~112 |
| Page view： 1123
Net amount： 768 |
Authors： |
Veli B. SHAKHMUROV; |
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| Abstract： |
This study focuses on the anisotropic Besov-Lions type spaces $Bp,\thetal( \Omega ;E_{0},E) $ associated with Banach spaces $E_{0}$ and $E$. Under certain conditions, depending on $l=(l1,l2,\cdots ,ln) $ and $\alpha =( \alpha1,\alpha 2,\cdots ,\alphan) ,$ the most regular class of interpolation space $E\alpha$ between $E0$ and $E$ are found so that the mixed differential operators $D\alpha$ are bounded and compact from $Bp,\thetal+s( \Omega ;E0,E) $ to $Bp,\thetas( \Omega ;E\alpha).$ 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. |
Keywords： |
Embedding theorems, Banach-valued function spaces, Differential-operator equations, B-Separability, Operatorvalued Fourier multipliers, Interpolation of Banach spaces |
Classification： |
42A45, 54C25, 34B10, 35J25 |
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