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Commutators on Half-Spaces

Authors:	Jie?Miao mailto:miao@csm.astate.edu" title=" miao@csm.astate.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Computer Science and Mathematics, State University, P.O. Box 70, Arkansas, Arkansas 72467, USA

Abstract:	We study the boundedness and compactness of commutators on $L^p(mathbb{R}^n_+, dv)$ , where and are defined by and respectively. If satisfies some upper and lower estimates, then we obtain a necessary and sufficient conditionfor to be bounded or compact on $L^p(mathbb{R}^n_+, dv)$ for .The reproducing kernel of the harmonic Bergman space of can be shownto satisfy all the required estimates. Our result is the real variable analogueof the complex variable one for commutators associated with an analytic reproducingkernel.

Keywords:	Primary: 47B35 Secondary: 47B32 47B47
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