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- W3049187851 abstract "Let $mu$ be a positive Borel measure on the positive real axis. We study the integral operator $$ mathcal{H}_{mu}(f)(z)=int_{0}^{infty}frac{1}{t}fleft(frac{z}{t}right),dmu(t),quad zin mathbb{C},, $$ acting on the Fock spaces $F^{p}_{alpha}$, $pin [1,infty],,alpha >0$. Its action is easily seen to be a coefficient multiplication by the moment sequence $$ mu_n= int_{1}^{infty}frac{1}{t^{n+1}},dmu(t) . $$ We prove that begin{equation*} ||mathcal{H}_{mu}||_{F^{p}_{alpha}to F^{p}_{alpha}}=sup_{ninmathbb{N}}mu_n,,,,,,1leq pleq infty,,. end{equation*} A little-o,condition describes the compactness of $mathcal{H}_{mu}$ on every $F^{p}_{alpha},,pin (1,infty )$. In addition, we completely characterize the Schatten class membership of $mathcal{H}_{mu}$." @default.
- W3049187851 created "2020-08-21" @default.
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- W3049187851 date "2020-08-15" @default.
- W3049187851 modified "2023-09-27" @default.
- W3049187851 title "Hausdorff operators on Fock Spaces." @default.
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