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Continuity and differentiability properties of the Nemitskii operator in Hölder spaces

Published online by Cambridge University Press:  18 May 2009

Rita Nugari
Rita Nugari
Affiliation:
Università dègli Studi della Calabria, Dipartimento di Matematica, 87036 Arcavacata di Rende (Cosenza), Italy
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Let ℝn be the n-dimensional Euclidean space with the usual norm denoted by |·| In what follows 蒆 will denote an open bounded subset of ℝn, and its closure.

For α ∊(0,1], is the space of all functions such that:

is called the Holder space with exponent a and is a Banach space when endowed with the norm:

where ‖u‖∞ is, as usual, defined by:

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 59 - 65
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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