Shakhmurov, Veli; Musaev, Hummet Maximal regular convolution-differential equations in weighted Besov spaces. (English) Zbl 1474.34401 Appl. Comput. Math. 16, No. 2, 190-200 (2017). Summary: By using Fourier multiplier theorems, the maximal regularity properties of abstract convolution differential equations in weighted Besov spaces are investigated. It is shown that the corresponding convolution differential operators are positive and generate analytic semigroups in abstract Besov spaces. Then, the well-posedness of the Cauchy problem for parabolic convolution – operator equation is established. Moreover, these results are used to establish maximal regularity properties for system of integro-differential equations of finite and infinite orders. Cited in 8 Documents MSC: 34G10 Linear differential equations in abstract spaces 34G20 Nonlinear differential equations in abstract spaces 45J05 Integro-ordinary differential equations 30H25 Besov spaces and \(Q_p\)-spaces Keywords:positive operators; vector valued Besov spaces; Sobolev-Linos type spaces; operator-valued multipliers; convolution equations PDFBibTeX XMLCite \textit{V. Shakhmurov} and \textit{H. Musaev}, Appl. Comput. Math. 16, No. 2, 190--200 (2017; Zbl 1474.34401) Full Text: Link