7 papers
Fractional gradients and nonlocal PDEs in variable exponent spaces
Susana Moura, Cornelia Schneider
We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy…
Compact embeddings of generalised Morrey smoothness spaces on bounded domains
Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak
We study embeddings within different scales of generalised smoothness Morrey spaces defined on bounded smooth domains, i.e., in , $\mathcal{E}^s_{φ,p,q}(Ω…
Embeddings of generalised Morrey smoothness spaces
Dorothee D. Haroske, Zhen Liu, Susana D. Moura +1
We study embeddings between generalised Triebel-Lizorkin-Morrey spaces and within the scales of further generalised Morrey smoothness spac…
On a bridge connecting Lebesgue and Morrey spaces in view of their growth properties
Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak
We study unboundedness properties of functions belonging to generalised Morrey spaces and generalised Besov-Morrey spaces ${\mathcal N}^{s}_{φ,p…
Nuclear and compact embeddings in function spaces of generalised smoothness
Dorothee D. Haroske, Hans-Gerd Leopold, Susana D. Moura +1
We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain . This covers, in particular, the well-known s…
Wavelet decomposition and embeddings of generalised Besov-Morrey spaces
Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak
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…
Some embeddings of Morrey spaces with critical smoothness
Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak
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…