On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces
Department
Mathematics
Document Type
Article
Publication Date
12-1-2021
Abstract
We present a unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Pólya and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemannian manifolds and derive the well-known Taikov and Hardy-Littlewood-Pólya inequalities for functions defined on the d-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of another class. In addition, we establish sharp Solyar type inequalities for unbounded closed operators with closed range.
Journal Title
Analysis Mathematica
Journal ISSN
01333852
Volume
47
Issue
4
First Page
709
Last Page
745
Digital Object Identifier (DOI)
10.1007/s10476-021-0104-8