Toeplitz-Hankel type operators on product spaces

Via a series of orthogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on U×U (U is the upper half-plane) with the measurey ^a ₁ y ^a ₁ dx ₁ dx ₂ dx ₁ dx ₂ is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness, S_p properties of them are established. Research was supported by the National Natural Science Foundation of China.