TY - JOUR
T1 - Local Tb theorems and hardy inequalities
AU - Auscher, Pascal
AU - Routin, Eddy
PY - 2013/1
Y1 - 2013/1
N2 - In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2, with an additional weak boundedness type hypothesis, which incorporates some Hardy type inequalities. The latter can be obtained from some geometric conditions on the homogeneous space. For example, we prove that the monotone geodesic property of Tessera suffices.
AB - In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2, with an additional weak boundedness type hypothesis, which incorporates some Hardy type inequalities. The latter can be obtained from some geometric conditions on the homogeneous space. For example, we prove that the monotone geodesic property of Tessera suffices.
KW - Hardy type inequalities
KW - Local Tb theorem
KW - Singular integral operators
KW - Space of homogeneous type
UR - http://www.scopus.com/inward/record.url?scp=84872597398&partnerID=8YFLogxK
U2 - 10.1007/s12220-011-9249-1
DO - 10.1007/s12220-011-9249-1
M3 - Article
SN - 1050-6926
VL - 23
SP - 303
EP - 374
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 1
ER -