D. Edmunds

activity

20072021

most citedBoundedness of classical operators on rearrangement-invariant spaces

30 citations · 37 across the 9 of their papers we have counts for

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7 papers · 1 filter

math.FA2021★ 1 cited

Almost-compact and compact embeddings of variable exponent spaces

D. E. Edmunds, A. Gogatishvili, A. Nekvinda

Let $Ω$ be an open subset of $R^{N}$ , and let $p, q : Ω \to [1, \infty]$ be measurable functions. We give a necessary and sufficient condition for the…

math.FA2020★ 5 cited

Measure of noncompactness of Sobolev embeddings on strip-like domains

David E. Edmunds, Jan Lang, Zdeněk Mihula

We compute the precise value of the measure of noncompactness of Sobolev embeddings $W_{0}^{1, p} (D) ↪ L^{p} (D)$ , $p \in (1, \infty)$ , on strip-like domains $D$ of the form $\…

math.FA2019★ 30 cited

Boundedness of classical operators on rearrangement-invariant spaces

David E. Edmunds, Zdeněk Mihula, Vít Musil +1

We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fracti…

math.FA2017

Construction of function spaces close to $L^{\infty}$ with associate space close to $L^{1}$

David Edmunds, Amiran Gogatishvili, Tengiz Kopaliani

The paper introduces a variable exponent space $X$ which has in common with $L^{\infty} ([0, 1])$ the property that the space $C ([0, 1])$ of continuous functions on $[0, 1]$ is a close…

math.FA2015

Some $s$ -numbers of an integral operator of Hardy type in Banach function spaces

David Edmunds, Amiran Gogatishvili, Tengiz Kopaliani +1

Let $s_{n} (T)$ denote the $n$ th approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator $T$ given by $$ Tf(x)=v(x)\int_{a}^{x}u(t)f(…

math.FA2015

Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator

David E. Edmunds, Jan Lang

Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for th…