By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related to the beta function is proved to be the best possible. As applications, the case of the homogeneous kernel, the operator expressions, and a few corollaries are considered.
No takes yet. Share an insight, caveat, or question.
Xin et al. (2018) studied this question.
Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context: