Products of Toeplitz and Hankel Operators on Fock Spaces

Abstract

In this paper, we characterize bounded Toeplitz product $$T_fT_{g}$$ and Hankel product $$H_f^{*}H_g$$ on Fock space $$F_{\alpha }^2$$ for two polynomials f and g in z and $${\overline{z}}$$ . As a consequence, we obtain when Toeplitz operator $$T_f$$ or Hankel operator $$H_f$$ with the polynomial symbol f in z and $${\overline{z}}$$ is bounded.