Maximal characterisation of local Hardy spaces on locally doubling manifolds
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AbstractWe prove a radial maximal function characterisation of the local atomic Hardy space $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to $${{\mathfrak {h}}}^1(M)$$ h 1 ( M ) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama.
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2009 ◽
Vol 346
(2)
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pp. 307-333
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2018 ◽
Vol 43
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pp. 47-87
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2012 ◽
Vol 23
(09)
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pp. 1250095
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2013 ◽
Vol 1
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pp. 147-162
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