Geometric & Functional Analysis GAFA

, Volume 2, Issue 2, pp 137–172 | Cite as

Markov chains, Riesz transforms and Lipschitz maps



it is shown that a version of Maurey's extension theorem holds for Lipschitz maps between metric spaces satisfying certain geometric conditions, analogous to type and cotype. As a consequence, a classical Theorem of Kirszbraun can be generalised to include maps intoL p , 1<p<2. These conditions describe the wandering of symmetric Markov processes in the spaces in question. Estimates are obtained for the root-mean-square wandering of such processes in theL p spaces. The duality theory for these geometric conditions (in normed spaces) is shown to be closely related to the behavior of the Riesz transforms associated to Markov chains. Several natural open problems are collected in the final chapter.


Markov Chain Open Problem Markov Process Normed Space Duality Theory 
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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • K. Ball
    • 1
    • 2
  1. 1.Department of MathematicsT.A.M.U.College StationUSA
  2. 2.Department of MathematicsU.C.L.LondonEngland

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