Construction Conditions and Applications of a Hilbert-Type Multiple Integral Inequality Involving Multivariable Upper Limit Functions and Higher-Order Partial Derivatives
Year: 2025
Type: article
Abstract: Hilbert-type inequalities derive from the classical Hilbert inequality, and their theoretical work has key applications not only in operator theory but also in various analytic disciplines. In this paper, we have achieved the parametric conditions required for the construction of such inequalities, as well as the expressions for the optimal constant factors. Through the utilization of the construction theorem for Hilbert-type multiple integral inequalities with homogeneous kernels, our investigation centers on a Hilbert-type multiple integral inequality that involves multivariable upper limit functions and higher-order partial derivatives. Furthermore, we apply these results to discuss the boundedness and operator norms of integral operators with identical kernels.
Source: Axioms
Authors: Yong Hong, Qian Zhao, Zhihong Zhao
Institutions: Guangzhou Huashang College, Beijing Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Award: G7496552270
OpenAlex ID: W4410211716