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Continuity and differentiability properties of the Nemitskii operator in Hölder spaces
Published online by Cambridge University Press: 18 May 2009
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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:
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- Copyright © Glasgow Mathematical Journal Trust 1988
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