Hankel- and Toeplitz-Type Operators on the Unit Ball1

Let Bm be the unit ball in the m-dimensional complex plane Cm with the weighted measure dμα z = α + 1 α + 2 · · · α + m πm 1 − z 2 αdm z α > −1 From the viewpoint of the Cauchy–Riemann operator we give an orthogonal direct sum decomposition for L2 Bm dμα z , i.e., L2 Bm dμα z = ⊕n∈Z+ σ∈ Aσ n , where the components A + + + 0 and A − − − 0 are just the weighted Bergman and conjugate Bergman spaces, respectively.Using the simplex polynomials from T.H.Koornwinder and A.L.Schwartz (1997, Constr. Approx 13, 537–567), we obtain an orthogonal basis for every subspace.As an application of the orthogonal decomposition, we define the Hankel- and Toeplitz-type operators and discuss Sp-criteria for these kinds of operators.