✦ LIBER ✦

Approximate identities in variable Lp spaces

✍ Scribed by D. Cruz-Uribe SFO; A. Fiorenza

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 202 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410479

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We give conditions for the convergence of approximate identities, both pointwise and in norm, in variable L ^p^ spaces. We unify and extend results due to Diening [8], Samko [18] and Sharapudinov [19]. As applications, we give criteria for smooth functions to be dense in the variable Sobolev spaces, and we give solutions of the Laplace equation and the heat equation with boundary values in the variable L ^p^ spaces. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Approximation by rational operators in L

Approximation by rational operators in Lp spaces

✍ Dansheng Yu; Songping Zhou 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 193 KB

## Abstract The present paper introduces a kind of Kantorovich type Shepard operators. Complete results including direct and converse results, equivalence results are established. As Della Vecchia and Mastroianni ([4], [7]) did, our results involve a weighted modulus of smoothness related to step‐f

Singular operators in variable spaces Lp

Singular operators in variable spaces Lp (·)(Ω, ρ) with oscillating weights

✍ Vakhtang Kokilashvili; Natasha Samko; Stefan Samko 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 189 KB

## Abstract We study the boundedness of singular Calderón–Zygmund type operators in the spaces __L__^__p__ (·)^(Ω, __ρ__) over a bounded open set in ℝ^__n__^ with the weight __ρ__ (__x__) = $ \prod ^m\_{k=1} $ __w__~__k__~ (|__x__ – __x__~__k__~ |), __x__~__k__~ ∈ $ \bar \Omega $, where __w__~__k

On Müntz Rational Approximation Rate in

On Müntz Rational Approximation Rate in Lp Spaces

✍ Wei Xiao; Songping Zhou 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 102 KB

On isometries in Lp spaces

✍ Juan Carlos Merlo 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 147 KB

Approximate decidability in euclidean sp

Approximate decidability in euclidean spaces

✍ Armin Hemmerling 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 368 KB

## Abstract We study concepts of decidability (recursivity) for subsets of Euclidean spaces ℝ^__k__^ within the framework of approximate computability (type two theory of effectivity). A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F

The Vervaat Process in Lp Spaces

✍ Miklós Csörgő; Ričardas Zitikis 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 251 KB

It is well known that, asymptotically, the appropriately normalized Vervaat process behaves like one half times the squared empirical process. Considering these two processes as elements of the L p -space, 1 p< , we give a complete description of the strong and weak asymptotic behaviour of the L p -