Quantitative property A, Poincaré inequalities, Lp-compression and Lp-distortion for metric measure spaces |
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Authors: | Romain Tessera |
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Institution: | (1) Department of Mathematics, Vanderbilt University, Stevenson Center, Nashville, TN 37240, USA |
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Abstract: | We introduce a quantitative version of Property A in order to estimate the L
p
-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to
be useful to yield upper bounds on the L
p
-distortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemannian manifolds.
We also introduce a general form of Poincaré inequalities that provide constraints on compressions, and lower bounds on distortion.
These inequalities are used to prove the optimality of some of our results.
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Keywords: | Uniform embeddings of metric spaces into Banach spaces Property A Poincare inequalities Hilbert compression Hilbert distortion |
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