TY - JOUR
T1 - The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel
AU - Wei, Huaying
AU - Matsuzaki, Katsuhiko
N1 - Funding Information:
Research supported by Japan Society for the Promotion of Science (KAKENHI 18H01125 and 21F20027)
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/11
Y1 - 2022/11
N2 - We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.
AB - We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.
KW - A-weight
KW - BMO function
KW - Beurling–Ahlfors extension
KW - VMO Teichmüller space
KW - Vanishing Carleson measure
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U2 - 10.1007/s00209-022-03104-6
DO - 10.1007/s00209-022-03104-6
M3 - Article
AN - SCOPUS:85137490245
SN - 0025-5874
VL - 302
SP - 1739
EP - 1760
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -