Spaces of Lipschitz and Hölder functions and their applications.

Kalton, Nigel J.. "Spaces of Lipschitz and Hölder functions and their applications.." Collectanea Mathematica 55.2 (2004): 171-217. <http://eudml.org/doc/44337>.

@article{Kalton2004,
abstract = {We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 &lt; α &lt; 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l∞. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if and only if M is finite-dimensional. We also study the (related) problem of when a quotient map Q: Y --&gt; X between two Banach spaces admits a section which is uniformly continuous on the unit ball of X.},
author = {Kalton, Nigel J.},
journal = {Collectanea Mathematica},
keywords = {Function spaces; Lipschitz space; Hölder spaces},
language = {eng},
number = {2},
pages = {171-217},
title = {Spaces of Lipschitz and Hölder functions and their applications.},
url = {http://eudml.org/doc/44337},
volume = {55},
year = {2004},
}

TY - JOUR
AU - Kalton, Nigel J.
TI - Spaces of Lipschitz and Hölder functions and their applications.
JO - Collectanea Mathematica
PY - 2004
VL - 55
IS - 2
SP - 171
EP - 217
AB - We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 &lt; α &lt; 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l∞. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if and only if M is finite-dimensional. We also study the (related) problem of when a quotient map Q: Y --&gt; X between two Banach spaces admits a section which is uniformly continuous on the unit ball of X.
LA - eng
KW - Function spaces; Lipschitz space; Hölder spaces
UR - http://eudml.org/doc/44337
ER -