arXiv subjects

Susana D. Moura

Publications and source records attributed to Susana D. Moura.

6 recordsLinked to original sources

arXiv2026

Compact embeddings of generalised Morrey smoothness spaces on bounded domains

We study embeddings within different scales of generalised smoothness Morrey spaces defined on bounded smooth domains, i.e., in $\mathcal{N}^s_{φ,p,q}(Ω)$, $\mathcal{E}^s_{φ,p,q}(Ω)$, $B^{s,φ}_{p,q}(Ω)$ and $F^{s,φ}_{p,q}(Ω)$ spaces. We prove sufficient conditions for continuity and compactness of the embeddings. In some cases the conditions are also necessary. We generalise and even improve some earlier results known for the classical smoothness Morrey spaces. Our approach is based on wavelet characterisation of the function spaces.

math.FA↗

arXiv2023

Embeddings of generalised Morrey smoothness spaces

We study embeddings between generalised Triebel-Lizorkin-Morrey spaces ${\mathcal E}^{s}_{φ,p,q}({\mathbb R}^d)$ and within the scales of further generalised Morrey smoothness spaces like ${\mathcal N}^{s}_{φ,p,q}({\mathbb R}^d)$, ${B}_{p,q}^{s,φ}({\mathbb R}^d)$ and ${F}_{p,q}^{s,φ}({\mathbb R}^d)$. The latter have been investigated in a recent paper by the first two authors (2023), while the embeddings of the scale ${\mathcal N}^{s}_{φ,p,q}({\mathbb R}^d)$ were mainly obtained in a paper of the first and last two authors (2022). Now we concentrate on the characterisation of the spaces ${\mathcal E}^{s}_{φ,p,q}({\mathbb R}^d)$. Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies' wavelets. Then we prove necessary and sufficient conditions for the embedding ${\mathcal E}^{s_1}_{φ_1,p_1,q_1}({\mathbb R}^d)\hookrightarrow {\mathcal E}^{s_2}_{φ_2,p_2,q_2}({\mathbb R}^d)$. We can also provide some almost final answer to the question when ${\mathcal E}^{s}_{φ,p,q}({\mathbb R}^d)$ is embedded into $C({\mathbb R}^d)$, complementing our recent findings in case of ${\mathcal N}^{s}_{φ,p,q}({\mathbb R}^d)$.

math.FA↗

arXiv2023

On a bridge connecting Lebesgue and Morrey spaces in view of their growth properties

We study unboundedness properties of functions belonging to generalised Morrey spaces ${\mathcal M}_{φ,p}({\mathbb R}^d)$ and generalised Besov-Morrey spaces ${\mathcal N}^{s}_{φ,p,q}({\mathbb R}^d)$ by means of growth envelopes. For the generalised Morrey spaces we arrive at the same three possible cases as for classical Morrey spaces $\mathcal{M}_{u,p}({\mathbb R}^d)$, i.e., boundedness, the $L_p$-behaviour or the proper Morrey behaviour for $p<u$, but now those cases are characterised in terms of the limit of $φ(t)$ and $t^{-d/p} φ(t)$ as $t \to 0^+$ and $t\to\infty$, respectively. For the generalised Besov-Morrey spaces the limit of $t^{-d/p} φ(t)$ as $t \to 0^+$ also plays a rôle and, once more, we are able to extend to this generalised spaces the known results for classical Besov-Morrey spaces, although some cases are not completely solved. In this context we can completely characterise the situation when ${\mathcal N}^{s}_{φ,p,q}({\mathbb R}^d)$ consists of essentially bounded functions only, and when it contains regular distributions only.

math.FA↗

arXiv2022

Nuclear and compact embeddings in function spaces of generalised smoothness

We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain $Ω\subset\mathbb{R}^d$. This covers, in particular, the well-known situation for spaces of Besov and Triebel-Lizorkin spaces defined on bounded domains as well as some first results for function spaces of logarithmic smoothness. In addition, we provide some new, more general approach to compact embeddings for such function spaces, which also unifies earlier results in different settings, including also the study of their entropy numbers. Again we rely on suitable wavelet decomposition techniques and the famous Tong result (1969) about nuclear diagonal operators acting in $\ell_r$ spaces, which we could recently extend to the vector-valued setting needed here.

math.FA↗

arXiv2020

Wavelet decomposition and embeddings of generalised Besov-Morrey spaces

We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets.

math.FA↗

arXiv2019

Some embeddings of Morrey spaces with critical smoothness

We study embeddings of Besov-Morrey spaces ${\cal N}^{s}_{u,p,q}}({\mathbb R}^d)$ and of Triebel-Lizorkin-Morrey spaces ${\cal E}^{s}_{u,p,q}}({\mathbb R}^d)$ in the limiting cases when the smoothness $s$ equals $s_0=d\max(1/u-p/u,0)$ or $s_{\infty}=d/u$, which is related to the embeddings in $L_1^{loc}({\mathbb R}^d)$ or in $L_\infty({\mathbb R}^d)$, respectively. When $s=s_0$ we characterise the embeddings in $L_1^{loc}({\mathbb R}^d)$ and when $s=s_{\infty}$ we obtain embeddings into Orlicz-Morrey spaces of exponential type and into generalised Morrey spaces.

math.FA↗