The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications

Abstract

In this paper, we establish equivalent parameter conditions for the validity of multiple integral half-discrete Hilbert-type inequalities with the nonhomogeneous kernel G(nλ1∥x∥m,ρλ2)G\left({n}^{{\lambda }_{1}}\parallel x{\parallel }_{m,\rho }^{{\lambda }_{2}}\hspace{-0.16em}) (λ1λ2>0{\lambda }_{1}{\lambda }_{2}\gt 0) and obtain best constant factors of the inequalities in specific cases. In addition, we also discuss their applications in operator theory.

Keywords

• multiple integral half-discrete hilbert-type inequality
• nonhomogeneous kernel
• equivalent parameter condition
• best constant factor
• operator norm
• bounded operator
• 26d15
• 47a07