Journal of Operator Theory
Volume 71, Issue 2, Spring 2014 pp. 381-410.
Invertible Toeplitz products, weighted norm
inequalities, and $\mathrm{A}_p$ weights
Authors:
Joshua Isralowitz
Author institution:SUNY Albany,
1400 Washington Ave.
Albany, NY,
12222, U.S.A.
Summary: In this paper, we characterize invertible Toeplitz
products on a number of
Banach spaces of analytic functions, including the weighted\break Bergman
space $L^p _\mathrm a (\mathbb{B}_n, \mathrm dv_\gamma)$, the Hardy space
$H^p(\partial \mathbb{D})$, and the standard 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. 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 H\"older inequality" of Zheng and
Stroethoff (\textit{J. Funct. Anal.}
\textbf{195}(2002), 48-70 and \textit{J. Operator Theory}
\textbf{59}(2008), 277-308) for $p = 2$ to the general case of $p > 1$.
DOI: http://dx.doi.org/10.7900/jot.2012apr10.1989
Keywords: Toeplitz operator, weighted norm inequalities, products of
Toeplitz operators
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