Embeddings of generalised Morrey smoothness spaces (Preprint)

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Type: Preprint
National /International: International
Title: Embeddings of generalised Morrey smoothness spaces
Publication Date: 2023-10-27
Authors: - Dorothee D. Haroske
- Zheng Liu
- Susana Domingues de Moura
- Leszek Skrzypczak
Abstract:

We study embeddings between generalised Triebel-Lizorkin-Morrey spaces Esφ,p,q(Rd) and within the scales of further generalised Morrey smoothness spaces like Nsφ,p,q(Rd), Bs,φp,q(Rd) and Fs,φp,q(Rd). The latter have been investigated in a recent paper by the first two authors (2023), while the embeddings of the scale Nsφ,p,q(Rd) were mainly obtained in a paper of the first and last two authors (2022). Now we concentrate on the characterisation of the spaces Esφ,p,q(Rd).
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 Es1φ1,p1,q1(Rd)Es2φ2,p2,q2(Rd). We can also provide some almost final answer to the question when Esφ,p,q(Rd) is embedded into C(Rd), complementing our recent findings in case of Nsφ,p,q(Rd).

Institution: arXiv:2310.18282
Online version: https://arxiv.org/abs/2310.18282
Download: Not available
 
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