SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS
As the homogeneous Triebel–Lizorkin space $\dot{F}_{p,q}^s$ and the space BMO are defined modulo polynomials and constants, respectively, we prove that BMO coincides with the realized space of $\dot{F}_{\infty, 2}^0$ and cannot be directly identified with $\dot{F}_{\infty, 2}^0$. In case $p <...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2024-05-01
|
| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=15111&lang=en |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | As the homogeneous Triebel–Lizorkin space $\dot{F}_{p,q}^s$ and
the space BMO are defined modulo polynomials and constants,
respectively, we prove that BMO coincides with the realized space
of $\dot{F}_{\infty, 2}^0$ and cannot be directly identified with $\dot{F}_{\infty, 2}^0$. In case $p < \infty$, we also prove that the realized space of $\dot{F}_{p,q}^{n/p}$ is strictly embedded into BMO. Then we deduce other results in this paper, that are extensions to homogeneous and inhomogeneous Besov spaces, $\dot{B}_{p,q}^s$ and $B_{p,q}^s$, respectively. We show embeddings between BMO and the classical Besov space $B_{\infty, \infty}^0$ in the first case and the realized spaces of $\dot{B}_{\infty, 2}^0$ and $\dot{B}_{\infty, \infty}^0$ in the second one. On the other hand, as an application, we discuss the acting of the Riesz operator $\mathscr{L}_{\beta}$ on BMO space, where we obtain embeddings related to realized versions of $\dot{B}_{\infty, 2}^{\beta}$ and $\dot{B}_{\infty, \infty}^{\beta}$. |
|---|---|
| ISSN: | 2306-3424 2306-3432 |