Weakly absolutely continuous functions without weak, but fractional weak derivatives

Let E be an infinite-dimensional Banach space and I be a compact interval of the real line. The aim of this paper is two-fold: On the one hand, we construct an example of a weakly absolutely continuous function taking its values in E that is nowhere weakly differentiable on I , but has weakly contin...

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Vydáno v:Journal of pseudo-differential operators and applications Ročník 10; číslo 4; s. 941 - 954
Hlavní autor: Salem, Hussein A. H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.12.2019
Springer Nature B.V
Témata:
Algebra
Analysis
Applications of Mathematics
Banach spaces
Continuity (mathematics)
Derivatives
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Partial Differential Equations
34G20
Pettis integrals
Fractional calculus
Orlicz spaces
26A33
ISSN:1662-9981, 1662-999X
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Shrnutí:Let E be an infinite-dimensional Banach space and I be a compact interval of the real line. The aim of this paper is two-fold: On the one hand, we construct an example of a weakly absolutely continuous function taking its values in E that is nowhere weakly differentiable on I , but has weakly continuous fractional weak derivatives of some critical orders less than one. This also holds for (nearly) all orders less than one if E failing cotype. We believe that this results are of independent interest and discuss it in a rather general setting. On the other hand, we establish some examples of weakly continuous functions taking its values in Gauge space fail to be pseudo differentiable on I , but have fractional-pseudo derivatives of “all” order less than one. An application will be given.
Bibliografie:ObjectType-Article-1
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ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-019-00274-6