7 research outputs found
On the Hardy-Littlewood-P\'olya and Taikov type inequalities for multiple operators in Hilbert spaces
We present unified approach to obtain sharp mean-squared and multiplicative
inequalities of Hardy-Littlewood-Poly\'a 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 Riemmanian manifolds and derive the well-known Taikov and
Hardy-Littlewood-Poly\'a inequalities for functions defined on -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 other class. In addition, we establish sharp Solyar-type
inequalities for unbounded closed operators with closed range