𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On NEMYTSKIJ Operators in Lp-Spaces of Abstract Functions

✍ Scribed by H. Goldberg; W. Kampowsky; F. Tröltzsch

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
620 KB
Volume
155
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper is concerned with continuity and differentiability of NEMYTSKIJ operators acting between spaces of summable abstract functions. In a first part, necessary and sufficient conditions for continuity are collected. Then main emphasis is given to sufficient conditions for differentiability in the sense of FRÉCHET and GÂTEAUX. Finally, second order differentiability is briefly discussed.

📜 SIMILAR VOLUMES

One-sided operators in Lp (x) spaces
One-sided operators in Lp (x) spaces
✍ David E. Edmunds; Vakhtang Kokilashvili; Alexander Meskhi 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 236 KB

## Abstract Boundedness of one‐sided maximal functions, singular integrals and potentials is established in __L__(__I__) spaces, where __I__ is an interval in **R**. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Composition operators on spaces of real
Composition operators on spaces of real analytic functions
✍ Paweł Domański; Michael Langenbruch 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 259 KB 👁 1 views

Let Ω1, Ω2 be open subsets of R d 1 and R d 2 , respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operator Cϕ : Using this result we characterize when A(Ω1) can be embedded topologically into A(Ω2) as

Inclusion Relations for Some Lp-Spaces o
Inclusion Relations for Some Lp-Spaces of Operator-Valued Functions
✍ L. Klotz 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 389 KB 👁 1 views

Let (Q, a, p) be a positive measure space and D ( p ) , 0 < p 5 00, the space of (equivalence classes of) functions which are p-integrable with respect to p. In a nice short paper [9] A. VILLANI stated necessary and sufficient conditions for the measure p such that inclusions of the form D ( p ) D (