TY - JOUR
T1 - Littlewood-Paley theory on metric spaces with non doubling measures and its applications
AU - Tan, Chao Qiang
AU - Li, Ji
PY - 2015/5/1
Y1 - 2015/5/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84939264069&partnerID=8YFLogxK
U2 - 10.1007/s11425-014-4950-8
DO - 10.1007/s11425-014-4950-8
M3 - Article
AN - SCOPUS:84939264069
SN - 1674-7283
VL - 58
SP - 983
EP - 1004
JO - Science China Mathematics
JF - Science China Mathematics
IS - 5
ER -