Littlewood-Paley theory on metric spaces with non doubling measures and its applications

The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling 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 re...

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Published inScience China. Mathematics Vol. 58; no. 5; pp. 983 - 1004
Main Authors Tan, ChaoQiang, Li, Ji
Format Journal Article
LanguageEnglish
Published Heidelberg Science China Press 01.05.2015
Subjects
Applications of Mathematics
China
Equivalence
Gaussian
Mathematical analysis
Mathematics
Mathematics and Statistics
Metric space
Theorems
upper doubling
Littlewood-Paley theory
28A05
weak growth condition
42B20
non-homogeneous space
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Summary:The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling 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, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-014-4950-8