NDLI: Hardy Spaces and bmo on Manifolds with Bounded Geometry

Content Provider	Springer Nature Link
Author	Taylor, Michael
Copyright Year	2008
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, L $^{ p }$ 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 L $^{ p }$-Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive estimates for wave equations.
Starting Page	137
Ending Page	190
Page Count	54
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	19
Issue Number	1
e-ISSN	1559002X
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-10-25
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hardy space BMO Pseudodifferential operators Riemannian manifolds Bounded geometry Pseudodifferential and Fourier integral operators on manifolds Elliptic equations on manifolds, general theory Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems Global Analysis and Analysis on Manifolds Dynamical Systems and Ergodic Theory Abstract Harmonic Analysis Fourier Analysis Convex and Discrete Geometry Differential Geometry
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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