可逆Toeplitz积、加权范数不等式和A ${}_p$权
Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weights
摘要：
本文刻画了若干解析函数的Banach空间上的可逆Toeplitz积，这些空间包括加权Bergman空间$L^p_a (\mathbb{B}_n, dv_γ)$，Hardy空间$H^p(\partial \mathbb{D})$，以及$p > 1$的加权Fock空间F ${}_α^p$.在我们的特征证明的共同工具将是理论的加权范数不等式和A ${}_p$型权重。此外，我们分析和比较各种A ${}_p$型条件，出现在我们的特征。最后，我们将Zheng和Stroethoff \cite{SZ1, SZ2}关于$p = 2$的“逆赫尔德不等式“推广到一般的$p > 1$情形.
英文摘要：
In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_γ)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted Fock space F${}_α^p$ 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 Hölder inequality" of Zheng and Stroethoff \cite{SZ1, SZ2} for $p = 2$ to the general case of $p > 1$.
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