36 citations · 127 across the 11 of their papers we have counts for
12 papers
A Hausdorff-measure boundary element method for acoustic scattering by fractal screens
António M. Caetano, Simon N. Chandler-Wilde, Andrew Gibbs +2
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application o…
Density results for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets
António Caetano, David P. Hewett, Andrea Moiola
We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) fo…
Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces
António Caetano, Henning Kempka
We continue the study of the variable exponent Morreyfied Triebel-Lizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We…
Variable exponent Triebel-Lizorkin-Morrey spaces
António Caetano, Henning Kempka
We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Little…
Variable exponent Besov-Morrey spaces
Alexandre Almeida, António Caetano
In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and…
Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
Alexandre Almeida, António Caetano
In this article we study atomic and molecular decompositions in -microlocal Besov and Triebel--Lizorkin spaces with variable integrability. We show that, in most cases, the conv…