Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weights

Details Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weights Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weights

2011-09-01

arxiv.org/abs/1109.0306v2

Mathematics

Classical Analysis and ODEs

v1: 31 pages, no figures, submitted. v2: 34 pages, no figures, minor changes and additions made, submitted

Scientific paper

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted Fock 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 A${}_p$ type weights. Moreover, we analyze and compare the various A${}_p$ type conditions that arise in our characterizations. Finally, we extend the "reverse H\"older inequality" of Zheng and Stroethoff \cite{SZ1, SZ2} for $p = 2$ to the general case of $p > 1$.

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