INVERTIBLE TOEPLITZ PRODUCTS, WEIGHTED NORM INEQUALITIES, AND Ap WEIGHTS

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including the weighted Bergman space L-a(p) (B-n, dv(gamma)), the Hardy space H-P (partial derivative D), and the standard weighted Pock space F-alpha(p) for p > 1. The common tool in the proofs of our characterizations will be the theory of weighted norm inequalities and Ap type weights. Furthermore, we prove weighted norm inequalities for the Fock projection, and compare the various Ap type conditions that arise in our results. Finally, we extend the "reverse Holder inequality" of Zheng and Stroethoff (J. Funct. Anal. 195(2002), 48-70 and J. Operator Theory 59(2008), 277-308) for p = 2 to the general case of p> 1.