Small Hankel operators between Fock spaces

ABSTRACT

Given f in the Fock space $F_{\alpha }^{\infty }$, for all possible $1\le p,q<\infty$, we characterize the boundedness (and compactness) of the small Hankel operator $h_{\overline{f}}$ from $F_{\alpha }^p$ to ${\overline{F}}_{\alpha }^q$. As an application, we obtain the norm estimates of the Hankel form $T_b^{\alpha }(·,·)$ acting on $F_{\alpha }^p\times F_{\alpha }^q$ with $1<p,q<\infty$.

KEYWORDS:

• Fock spaces
• small Hankel operators
• boundedness
• compactness

AMS SUBJECT CLASSIFICATIONS:

• 47B38
• 32A37

Acknowledgements

The authors express their thanks to the referee for his (her) careful reading and valuable suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11771139], [grant number 11571105], [grant number 11601149]; Natural Science Foundation of Zhejiang Province [grant number LY15A010014].