PRODUCT OF WEIGHTED HANKEL AND WEIGHTED TOEPLITZ OPERATORS

In this paper, we discuss some properties of the weighted Hankel operator H-psi(beta) and describe the conditions on which the weighted Hankel operator H-psi(beta) and weighted Toeplitz operator T-psi(beta), with phi,psi epsilon L-infinity (beta) on the space H-2 (beta), beta = {beta(n)}(n) subset of Z being a sequence of positive numbers with beta(0) = 1, commute. It is also proved that if a non- zero weighted Hankel operator H-psi(beta) commutes with T-psi(beta) , which is not a multiple of the identity, then H-psi(beta)= mu T-phi(beta), for some mu epsilon C.