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Commutators on Half-Spaces

Authors:	Email author" target="_blank">Jie?Miao Email author

Institution:	(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 $I_kg](x) = \int_H k(x,y)g(y)\, dv(y)$ respectively. If satisfies some upper and lower estimates, then we obtain a necessary and sufficient condition for to be bounded or compact on $L^p(\mathbb{R}^n_+, dv)$ for $1 < p < \infty$ . The reproducing kernel of the harmonic Bergman space of can be shown to satisfy all the required estimates. Our result is the real variable analogue of the complex variable one for commutators associated with an analytic reproducing kernel.

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