# Spaces of Lipschitz and Hölder functions and their applications.

Collectanea Mathematica (2004)

- Volume: 55, Issue: 2, page 171-217
- ISSN: 0010-0757

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topKalton, 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 < α < 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 --> 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 < α < 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 --> 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 -

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