Invertible toeplitz products, weighted norm inequalities, and A_p weights

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including the weighted Bergman space L^p_a (B_n, dv_γ), the Hardy space H^p(∂D), and the standard weighted Fock space F^p_α for p > 1. The common tool in the proofs of our characterizations will be the theory of weighted norm inequalities and A_p type weights. Furthermore, we prove weighted norm inequalities for the Fock projection, and compare the various A_p type conditions that arise in our results. Finally, we extend the "reverse Hölder 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.