Local Riesz Transform and Local Hardy Spaces on Riemannian Manifolds with Bounded Geometry

被引：3
|
作者：
Meda, Stefano [1 ]
Veronelli, Giona [1 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi 55, I-20125 Milan, Italy
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 02期
关键词：
Local Hardy space; Local Riesz transform; Bounded geometry; Locally doubling manifolds; Potential analysis on strips; HARMONIC-ANALYSIS; H-1; OPERATORS; BMO; LAPLACIAN;
D O I：
10.1007/s12220-021-00810-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that if tau is a large positive number, then the atomic Goldberg-type space h(1)(N) and the space h(R tau)(1) (N) of all integrable functions on N of which local Riesz transform R-tau is integrable, are the same space on any complete noncompact Riemannian manifold N with Ricci curvature bounded from below and positive injectivity radius. We also relate h(1)(N) to a space of harmonic functions on the slice N x (0, delta) for delta > 0 small enough.
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页数：57
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