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VOL. 31 | 2001 Hardy Spaces, Carleson Measures and a Gradient Estimate for Harmonic Functions on Negatively Curved Manifolds

Abstract

In this paper we study Hardy spaces, BMO, Carleson measures, Green potential and Bloch functions on a Cartan-Hadamard manifold $M$ of pinched negative curvature. Further, using our results on Carleson measure and BMO, we give a gradient estimate for harmonic functions on $M$. It is different from Yau's gradient estimates, and is applied to the existence problem of harmonic Bloch functions described in §10. We deal also with boundary behavior of harmonic Bloch functions on $M$.

Information

Published: 1 January 2001
First available in Project Euclid: 29 December 2018

zbMATH: 1011.31005
MathSciNet: MR1865086

Digital Object Identifier: 10.2969/aspm/03110001

Rights: Copyright © 2001 Mathematical Society of Japan

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