Operator-valued fourier multipliers in vector-valued function spaces and application

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ŞAHMUROV V.

Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences, vol.40, no.4, pp.153-174, 2020 (Scopus)

• Publication Type: Article / Article
• Volume: 40 Issue: 4
• Publication Date: 2020
• Journal Name: Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences
• Journal Indexes: Scopus
• Page Numbers: pp.153-174
• Keywords: Abstract differential equations, Banach space-valued functions, Embedding of abstract weighted spaces, Interpolation of Banach spaces, Operator-valued multipliers
• Open Archive Collection: Article
• Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The operator-valued Fourier multiplier theorems in E-valued weighted Lebesgue and Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces Bp,q,γl,s (Ω; E0, E), where E0, E are two Banach spaces and E0 ⊂ E. The most regular class of interpolation space Eα, between E0 and E are found such that the mixed differential operator Dα is bounded from Bp,q,γl,s (Ω; E0, E) to Bp,q,γs (Ω; Eα ) and Ehrling-Nirenberg-Gagliardo type sharp estimates are established. By using these results the Bp,q,γ −separabilitys properties of degenerate differential operators are studied.