JournalszaaVol. 31, No. 1pp. 93–124

Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters I

  • Martin Väth

    Czech Academy of Sciences, Prague, Czech Republic
Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters I cover
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Abstract

For a given single- or multivalued function ff and "atoms'' SiS_i, let Sf(λ,x)S_f(\lambda,x) be the set of all measurable selections of the function sf(λ,s,x(s))s\mapsto f(\lambda,s,x(s)) which are constant on each SiS_i. Continuity and differentiability of such operators are studied in spaces of measurable functions containing ideal, Orlicz and LpL_p spaces with new results for the parameter-dependent case even for single-valued superposition operators without atoms. A motivation is to apply the results for variant of such maps SfS_f in %%% here alteration

spaces in the second part of this article [Z. Anal. Anwend. 31 (2011) (to appear)].

Cite this article

Martin Väth, Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters I. Z. Anal. Anwend. 31 (2012), no. 1, pp. 93–124

DOI 10.4171/ZAA/1450