Continuity and differentiability of multivalued superposition operators with atoms and parameters I

0376652 - MÚ 2013 RIV DE eng J - Journal Article
Väth, Martin
Continuity and differentiability of multivalued superposition operators with atoms and parameters I.
Zeitschrift für Analysis und Ihre Anwendungen. Roč. 31, č. 1 (2012), s. 93-124. ISSN 0232-2064. E-ISSN 1661-4534
R&D Projects: GA AV ČR IAA100190805
Institutional research plan: CEZ:AV0Z10190503
Keywords : superposition operator * Nemytskij operator * multivalued map
Subject RIV: BA - General Mathematics
Impact factor: 0.620, year: 2012
http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=31&iss=1&rank=6

For a given single- or multivalued function f and "atoms'' S i , let S f (λ,x) be the set of all measurable selections of the function sf(λ,s,x(s)) which are constant on each S i . Continuity and differentiability of such operators are studied in spaces of measurable functions containing ideal, Orlicz and L 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 S f in Sobolev spaces in the second part of this article.
Permanent Link: http://hdl.handle.net/11104/0209001