Sharp Lp -Regular Nonlocal Differential Operators and Applications
Complex Analysis and Operator Theory, vol.19, no.3, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 19 Issue: 3
- Publication Date: 2025
- Doi Number: 10.1007/s11785-025-01663-0
- Journal Name: Complex Analysis and Operator Theory
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Keywords: Abstract weighted spaces, Convolution equations, Fractional differential equations, Integro-differential equations, Operator-valued multipliers, Sectorial operators
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: No
Abstract
The maximal regularity properties of a fractional anisotropic elliptic equation are investigated. The equation involves an abstract linear operator A in Fourier type Banach space E and convolution terms. We find the sufficient conditions that guarantee the separability of this problems in E-valued weighted Lp spaces. We prove that an anisotropic elliptic operator generated by this problem is sectorial and generates an analytic semigroup. In application, the maximal regularity properties of the Cauchy problem for degenerate abstract anisotropic parabolic equation and the boundary value problem for anisotropic elliptic convolution equation are obtained in mixed Lp norms.