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math.FA2023
A variant of Hilbert's inequality and the norm of the Hilbert Matrix on
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}^…
math.FA2020
Hausdorff operators on Fock Spaces
Petros Galanopoulos, Georgios Stylogiannis
Let be a positive Borel measure on the positive real axis. We study the integral operator $$ \mathcal{H}_μ(f)(z)=\int_{0}^{\infty}\frac{1}{t}f\left(\frac{z}{t}\right)\,dμ(t),\q…