Invertible Toeplitz products, weighted norm inequalities, and Aₚ weights

الأصل · EN

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space Lᵖₐ (Bₙ, dvγ), the Hardy space Hᵖ(∂ D), and the weighted Fock space Fαᵖ for p > 1. The common tool in the proofs of our characterizations will be the theory of weighted norm inequalities and Aₚ type weights. Moreover, we analyze and compare the various Aₚ type conditions that arise in our characterizations. Finally, we extend the "reverse Hölder inequality" of Zheng and Stroethoff SZ1, SZ2 for p = 2 to the general case of p > 1.