Abstract
For 1 ≤ p < ∞ we introduce a notion of “p-mean oscillation” on ℂn in terms of the ϱ metric induced by reproducing kernel of \(F_\Psi ^2\). It is shown that the densely-defined Hankel operators \({H_f},{H_{\bar f}}:F_\Psi ^p \to L_\Psi ^p\) are simultaneously bounded if and only if f is of bounded “p-mean oscillation”. Furthermore, it is also shown that the densely-defined Hankel operators \({H_f},{H_{\bar f}}:F_\Psi ^p \to L_\Psi ^p\) are simultaneously compact if and only if f is of vanishing “p-mean oscillation”. Here the weight Ψ is a positive function of logarithmic growth satisfying certain suitable conditions.
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Supported by NNSF of China (Grant No. 11971125)
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Tu, Z.H., Wang, X.F. Mean Oscillation and Hankel Operators on Fock-type Spaces. Acta. Math. Sin.-English Ser. 37, 1089–1108 (2021). https://doi.org/10.1007/s10114-021-0526-z
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DOI: https://doi.org/10.1007/s10114-021-0526-z