Journal of Geometric Analysis

, Volume 19, Issue 1, pp 137–190 | Cite as

Hardy Spaces and bmo on Manifolds with Bounded Geometry

Article

Abstract

We develop the theory of the “local” Hardy space \(\mathfrak{h}^{1}(M)\) and John-Nirenberg space \(\mathop{\mathrm{bmo}}(M)\) when M is a Riemannian manifold with bounded geometry, building on the classic work of Fefferman-Stein and subsequent material, particularly of Goldberg and Ionescu. Results include \(\mathfrak{h}^{1}\)\(\mathop{\mathrm{bmo}}\) duality, Lp estimates on an appropriate variant of the sharp maximal function, \(\mathfrak{h}^{1}\) and bmo-Sobolev spaces, and action of a natural class of pseudodifferential operators, including a natural class of functions of the Laplace operator, in a setting that unifies these results with results on Lp-Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive estimates for wave equations.

Keywords

Hardy space BMO Pseudodifferential operators Riemannian manifolds Bounded geometry 

Mathematics Subject Classification (2000)

58J40 58J05 46E35 

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Copyright information

© Mathematica Josephina, Inc. 2008

Authors and Affiliations

  1. 1.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

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