The distance in Morrey spaces to $C^{\infty}_{\mathrm{comp}}$
Abstract
In this paper, we characterize the distance between a function $f$ and the set $C^{\infty}_{\mathrm{comp}}(\mathbb{R}^d)$ in generalized Morrey space $L_{p,\phi}(\mathbb{R}^d)$ with variable growth condition. We also prove that the bi-dual of $\overline{C^{\infty}_{\mathrm{comp}}(\mathbb{R}^d)}^{L_{p,\phi}(\mathbb{R}^d)}$ is $L_{p,\phi}(\mathbb{R}^d)$. As an application of the characterization of the distance we show the boundedness of Calderón-Zygmund operators on $\overline{C^{\infty}_{\mathrm{comp}}(\mathbb{R}^d)}^{L_{p,\phi}(\mathbb{R}^d)}$. By the duality, we also see that these operators are bounded on its dual and bi-dual spaces.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Advanced Mathematical Physics Problems
Advanced Topology and Set Theory
Publication details
- Journal / source
- Hiroshima Mathematical Journal
- Publisher
- Hiroshima University - Department of Mathematics
- Volume
- 56
- Issue
- 2
- Pages
- 127–151
- Publication date
- 1 July 2026
- Language
- EN