Calder¨®n reproducing formulas and new Besov spaces associated with operators

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• 作者：Huy-Qui Bui^a ; ^{huy-qui.bui@canterbury.ac.nz} ; Xuan Thinh Duong^b ; ^{xuan.duong@mq.edu.au} ; Lixin Yan^c ; ^{mcsylx@mail.sysu.edu.cn}
• 关键词：42B30 ; 42B35 ; 46E35 ; 47F05
• 刊名：Advances in Mathematics
• 出版年：2012
• 出版时间：1 March 2012
• 年：2012
• 卷：229
• 期：4
• 页码：2449-2502
• 全文大小：362 K

文摘

Let L be the generator of an analytic semigroup whose heat kernel satisfies an upper bound of Poisson type acting on where is a (possibly non-doubling) space of polynomial upper bound on volume growth. The aim of this paper is to introduce a new class of Besov spaces associated with the operator L so that when L is the Laplace operator ??or its square root acting on the Euclidean space , the new Besov spaces are equivalent to the classical Besov spaces. Depending on the choice of L, the new Besov spaces are natural settings for generic estimates for certain singular integral operators such as the fractional powers . Since our approach does not require the doubling volume property of the underlying space, it is applicable to any subset ¦¸ of Euclidean spaces without any smoothness requirement on the boundary. We will also develop a number of Calder¨®n reproducing formulas which play an important role in the theory of function spaces and are of independent interest. As an application, we study Besov spaces associated with Schr?dinger operators with non-negative potentials satisfying reverse H?lder estimates.