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 <...
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Petrozavodsk State University
2024-05-01
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| Series: | Проблемы анализа |
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| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=15111&lang=en |
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| author | B. Gheribi M. Moussai |
| author_facet | B. Gheribi M. Moussai |
| author_sort | B. Gheribi |
| collection | DOAJ |
| description | 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 $\dot{B}_{\infty, \infty}^{\beta}$. |
| format | Article |
| id | doaj-art-312d45e06bae40539b86af6e14efc29c |
| institution | Kabale University |
| issn | 2306-3424 2306-3432 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj-art-312d45e06bae40539b86af6e14efc29c2024-12-31T14:07:18ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322024-05-0113 (31)2254810.15393/j3.art.2024.15111SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONSB. Gheribi0M. Moussai1Laboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer Science, University of M’silaLaboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer Science, University of M’silaAs 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 $\dot{B}_{\infty, \infty}^{\beta}$.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=15111&lang=enbesov spaces𝐵𝑀𝑂 functionsrealizationstriebel– lizorkin spaces |
| spellingShingle | B. Gheribi M. Moussai SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS Проблемы анализа besov spaces 𝐵𝑀𝑂 functions realizations triebel– lizorkin spaces |
| title | SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS |
| title_full | SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS |
| title_fullStr | SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS |
| title_full_unstemmed | SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS |
| title_short | SOME EMBEDDINGS RELATED TO HOMOGENEOUS TRIEBEL–LIZORKIN SPACES AND THE BMO FUNCTIONS |
| title_sort | some embeddings related to homogeneous triebel lizorkin spaces and the bmo functions |
| topic | besov spaces 𝐵𝑀𝑂 functions realizations triebel– lizorkin spaces |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=15111&lang=en |
| work_keys_str_mv | AT bgheribi someembeddingsrelatedtohomogeneoustriebellizorkinspacesandthebmofunctions AT mmoussai someembeddingsrelatedtohomogeneoustriebellizorkinspacesandthebmofunctions |