# Journal of Operator Theory

Volume 84, Issue 1, Summer 2020 pp. 35-47.

Mixed products of Toeplitz and Hankel operators on the Fock space**Authors**: Pan Ma (1), Fugang Yan (2), Dechao Zheng (3), Kehe Zhu, (4)

**Author institution:**(1) School of Mathematics and Statistics, Central South University, Hunan 410083, China

(2) College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China, and Department of Mathematics and Statistics, SUNY, Albany, NY 12222, U.S.A. (3) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A. and Center of Mathematics, Chongqing University, Chongqing 401331, China

(4) Department of Mathematics and Statistics, SUNY, Albany, NY 12222, U.S.A. and Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China

**Summary:**For entire functions $f$ and $g$ we determine exactly when the product $H_{\overline f}T_{\overline g}$ of the Hankel operator $H_{\overline f}$ and the Toeplitz operator $T_{\overline g}$ is bounded on the Fock space $F^2_\alpha$. This solves a natural companion to Sarason's Toeplitz product problem.

**DOI:**http://dx.doi.org/10.7900/jot.2018dec10.2246

**Keywords:**Toeplitz operators, Hankel operators, Fock space, Berezin transform

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