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Symmetric properties of p-integrable Teichmüller spaces

Symmetric properties of p-integrable Teichmüller spaces We prove symmetric properties of the p-integrable subspaces $$T_p$$ T p of the universal Teichmüller space T,  for $$p>0.$$ p > 0 . The elements of $$T_p$$ T p are quasisymmetric automorphisms of the real line or of the unit circle, which have a q.c. extension with p-integrable complex dilatation with respect to the Poincaré metric. We show that $$T_p\subset T_S,$$ T p ⊂ T S , where $$T_S$$ T S is the symmetric Teichmüller space and that, in the case of the real line, $$T_p\subset T_0,$$ T p ⊂ T 0 , where $$T_0$$ T 0 is the little Teichmüller space. The proofs use properties of the boundary behavior of q.c maps such as uniform weak conformality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Symmetric properties of p-integrable Teichmüller spaces

Analysis and Mathematical Physics , Volume 8 (4) – Oct 31, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature Switzerland AG
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-018-0259-z
Publisher site
See Article on Publisher Site

Abstract

We prove symmetric properties of the p-integrable subspaces $$T_p$$ T p of the universal Teichmüller space T,  for $$p>0.$$ p > 0 . The elements of $$T_p$$ T p are quasisymmetric automorphisms of the real line or of the unit circle, which have a q.c. extension with p-integrable complex dilatation with respect to the Poincaré metric. We show that $$T_p\subset T_S,$$ T p ⊂ T S , where $$T_S$$ T S is the symmetric Teichmüller space and that, in the case of the real line, $$T_p\subset T_0,$$ T p ⊂ T 0 , where $$T_0$$ T 0 is the little Teichmüller space. The proofs use properties of the boundary behavior of q.c maps such as uniform weak conformality.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Oct 31, 2018

References