Continuity and differentiability of Nemytskii operators on the Hardy space\mathcal{H}^{1,1} (T^1 ) |
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Authors: | John F Toland |
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Institution: | (1) Department of Mathematical Sciences, University of Bath, BA2 7AY Bath, UK |
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Abstract: | Let
denote the Hardy space of real-valued functions on the unit circle with weak derivatives in the usual real Hardy space
. It is shown that when the weak derivative of a locally Lipschitz continuous functionf has bounded variation on compact sets the Nemytskii operatorF, defined byF(u)=f·u, maps
continuously into itself. A further condition sufficient for the continuous Fréchet differentiability ofF is then added. |
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Keywords: | |
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