Abstract
Abstract The main objective of this paper is a study of some new multidimensional Hilbert-type inequalities with a general homogeneous kernel in the whole plane. We derive a pair of equivalent inequalities, and we also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered. MSC:26D15.
Highlights
Hilbert’s inequality is one of the most significant weighted inequalities in mathematical analysis and its applications
Hilbert-type inequalities were discussed by numerous authors, who either reproved them using various techniques, or applied and generalized them in many different ways
2 Main results we develop an unified treatment of the Hilbert and Hardy-Hilbert-type inequalities with general homogeneous kernel
Summary
Hilbert’s inequality is one of the most significant weighted inequalities in mathematical analysis and its applications. Xin and Yang in [ ] proved Hilbert-type inequalities with the homogeneous kernel of degree – . The following inequalities hold and are equivalent: n n 2 Main results we develop an unified treatment of the Hilbert and Hardy-Hilbert-type inequalities with general homogeneous kernel.
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