A variant of Hilbert's inequality and the norm of the Hilbert Matrix on $K^p$

Vassilis Daskalogiannis, Petros Galanopoulos, Michael Papadimitrakis

We prove the nontrivial variant \[ \sum\limits_{m,n=1}^{\infty}\Big(\frac{n}{m}\Big)^{\frac{1}{q}-\frac{1}{p}}\frac{a_mb_n}{m+n-1}\leq\fracπ{\sin\fracπ{p}} \Big( \sum\limits_{m=1}^…