Hilbert-type inequalities with a product-type homogeneous kernel and Schur polynomials (Q837618)

The authors generalize some results by \textit{Z. Xie} and \textit{Z. Zheng} [J. Math. Anal. Appl. 339, No. 1, 324--331 (2008; Zbl 1130.26021)] concerning Hilbert-type inequalities for conjugate parameters and with the kernel \[ k(x,y)= (x + a^2y)^{-1}\cdot (x+b^2y)^{-1}\cdot (x+c^2y)^{-1}, \] where \(a>0\), \(b>0\), \(c>0.\) The generalization bases on Hilbert-type inequalities with a kernel that satisfies conditions which ensure that the obtained constants are the best possible ones.