TY - JOUR
T1 - Discretization and affine approximation in high dimensions
AU - Li, Sean
AU - Naor, Assaf
N1 - Funding Information:
∗S. L. was supported by NSF grant CCF-0832795. A. N. was supported by NSF grant CCF-0832795, BSF grant 2010021, and the Packard Foundation. Some of this work was completed when both authors were in residence at the MSRI Quantitative Geometry program. Received February 18, 2012 and in revised form May 9, 2012
PY - 2013/10
Y1 - 2013/10
N2 - Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite-dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets.
AB - Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite-dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets.
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U2 - 10.1007/s11856-012-0182-1
DO - 10.1007/s11856-012-0182-1
M3 - Article
AN - SCOPUS:84883790568
SN - 0021-2172
VL - 197
SP - 107
EP - 129
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -