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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1016/0165-0378(89)90193-9

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1869-1862

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LittlewoodPaley theory on metric spaces with non

Authors: ChaoQiang Tan Ji Li
Publish Date: 2014/12/29
Volume: 58, Issue: 5, Pages: 983-1004
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Abstract

The purpose of this paper is to extend the LittlewoodPaley theory to a geometrically doubling metric space with a nondoubling measure satisfying a weak growth condition Moreover we prove that our setting mentioned above is equivalent to the one introduced and studied by Hytönen 2010 in his remarkable framework ie the geometrically doubling metric space with a nondoubling measure satisfying a socalled upper doubling condition As an application we obtain the T1 theorem in this more general setting Moreover the Gaussian measure is also discussed

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