On the definition of some Banach spaces over bounded domains with irregular boundary

Details On the definition of some Banach spaces over bounded domains with irregular boundary On the definition of some Banach spaces over bounded domains with irregular boundary

2005-05-18

arxiv.org/abs/math/0505380v3

Mathematics

Functional Analysis

4 pages, AmSTeX; v2: Added: 'surjection' in Exa 1, subscript 'H\"o' in Exa 3. Removed: use of AC in Prop 2; v3: a reference up

Scientific paper

This note aims to clarify the interrelations of certain inequivalently
defined Banach spaces denoted by C^i(\bar\Omega) for a natural number i and a
bounded open set \Omega. We give some sufficient conditions for the equality of
these spaces, and present examples to show that the spaces indeed can be
unequal for \Omega having irregular boundary.

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