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We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms. 相似文献
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Mishko Mitkovski 《Advances in Mathematics》2010,224(3):1057-2545
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Mishko Mitkovski Daniel Suárez Brett D. Wick 《Integral Equations and Operator Theory》2013,75(2):197-233
In this paper we characterize the compact operators on the weighted Bergman spaces ${A^p_\alpha(\mathbb{B}_n)}$ when 1 < p < ∞ and α > ?1. The main result shows that an operator on ${A^p_\alpha(\mathbb{B}_n)}$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball. 相似文献
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In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces. 相似文献
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