Some product problem of Toeplitz and Hankel operators on the bidisk

Abstract

The paper focuses on some product problem of Toeplitz operator $T_{\psi }$ with pluriharmonic symbol ψ and Hankel operator $H_{\phi }$ with general φ on the Hardy space of the bidisk. It completely solves when $T_{\psi }$ commutes with $H_{\phi }$. Also, the product of $T_{\psi }$ and $H_{\phi }$ being another Toeplitz operator or Hankel operator is characterized.