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Some embeddings related to homogeneous Triebel–Lizorkin spaces and the $BMO$ functions
B. Gheribi, M. Moussai Laboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer Science, University of M'sila, PO Box 166 Ichebilia, 28000 M'sila, Algeria
Аннотация:
As the homogeneous Triebel–Lizorkin space $\dot F^{s}_{p, q}$ and the space $BMO$ are defined modulo polynomials and constants, respectively, we prove that $BMO$ coincides with the realized space of $\dot F^{0}_{\infty, 2}$ and cannot be directly identified with $\dot F^{0}_{\infty, 2}$. In case $p<\infty$, we also prove that the realized space of $\dot F^{n/p}_{p, q}$ is strictly embedded into $BMO$. Then we deduce other results in this paper, that are extensions to homogeneous and inhomogeneous Besov spaces, $\dot B^{s}_{p, q}$ and $B^{s}_{p, q}$, respectively. We show embeddings between $BMO$ and the classical Besov space $ B^{0}_{\infty, \infty}$ in the first case and the realized spaces of $\dot B^{0}_{\infty, 2}$ and $\dot B^{0}_{\infty, \infty}$ in the second one. On the other hand, as an application, we discuss the acting of the Riesz operator $\mathcal{I}_{\beta}$ on $BMO$ space, where we obtain embeddings related to realized versions of $\dot B^{\beta}_{\infty, 2}$ and $\dot B^{\beta}_{\infty, \infty}$.
Ключевые слова:
Besov spaces, $BMO$ functions, realizations, Triebel–Lizorkin spaces.
Поступила в редакцию: 03.11.2023 Исправленный вариант: 28.02.2024 Принята в печать: 23.03.2024
Образец цитирования:
B. Gheribi, M. Moussai, “Some embeddings related to homogeneous Triebel–Lizorkin spaces and the $BMO$ functions”, Пробл. анал. Issues Anal., 13(31):2 (2024), 25–48
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa397 https://www.mathnet.ru/rus/pa/v31/i2/p25
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