Geodesic
Function algebras of Besov and Triebel-Lizorkin-type
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1281-1300
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
DOI : 10.21136/CMJ.2023.0585-22
Classification : 42B25, 46E35
Keywords: Littlewood-Paley decomposition; Besov-type space; Triebel-Lizorkin-type space 
@article{10_21136_CMJ_2023_0585_22,
     author = {Bensaid, Fares and Moussai, Madani},
     title = {Function algebras of {Besov} and {Triebel-Lizorkin-type}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1281--1300},
     year = {2023},
     volume = {73},
     number = {4},
     doi = {10.21136/CMJ.2023.0585-22},
     zbl = {07790574},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0585-22/}
}
TY  - JOUR
AU  - Bensaid, Fares
AU  - Moussai, Madani
TI  - Function algebras of Besov and Triebel-Lizorkin-type
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 1281
EP  - 1300
VL  - 73
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0585-22/
DO  - 10.21136/CMJ.2023.0585-22
LA  - en
ID  - 10_21136_CMJ_2023_0585_22
ER  - 
%0 Journal Article
%A Bensaid, Fares
%A Moussai, Madani
%T Function algebras of Besov and Triebel-Lizorkin-type
%J Czechoslovak Mathematical Journal
%D 2023
%P 1281-1300
%V 73
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0585-22/
%R 10.21136/CMJ.2023.0585-22
%G en
%F 10_21136_CMJ_2023_0585_22
Bensaid, Fares; Moussai, Madani. Function algebras of Besov and Triebel-Lizorkin-type. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1281-1300. doi: 10.21136/CMJ.2023.0585-22

[1] Bensaid, F., Moussai, M.: Realizations of the homogeneous Besov-type spaces. Methods Appl. Anal. 26 (2019), 349-370. | DOI | MR | JFM

[2] Bergh, G., Löfström, J.: Interpolation Spaces: An Introduction. Grundlehren der mathematischen Wissenschaften 223. Springer, Berlin (1976). | DOI | MR | JFM

[3] Bourdaud, G., Moussai, M., Sickel, W.: Composition operators on Lizorkin-Triebel spaces. J. Funct. Anal. 259 (2010), 1098-1128. | DOI | MR | JFM

[4] Bourdaud, G., Moussai, M., Sickel, W.: Composition operators acting on Besov spaces on the real line. Ann. Mat. Pura Appl. (4) 193 (2014), 1519-1554. | DOI | MR | JFM

[5] Baraka, A. El: An embedding theorem for Campanato spaces. Electron. J. Differ. Equ. 66 (2002), Article ID 66, 17 pages. | MR | JFM

[6] Frazier, M., Jawerth, B.: Decomposition of Besov spaces. Indiana Univ. Math. J. 34 (1985), 777-799. | DOI | MR | JFM

[7] Moussai, M.: Composition operators on Besov algebras. Rev. Mat. Iberoam. 28 (2012), 239-272. | DOI | MR | JFM

[8] Moussai, M.: Realizations of homogeneous Besov and Triebel-Lizorkin spaces and an application to pointwise multipliers. Anal. Appl., Singap. 13 (2015), 149-183. | DOI | MR | JFM

[9] Moussai, M.: Composition operators on Besov spaces in the limiting case $s=1+1/p$. Stud. Math. 241 (2018), 1-15. | DOI | MR | JFM

[10] Peetre, J.: New Thoughts on Besov Spaces. Duke University Mathematics Series I. Duke University, Durham (1976). | MR | JFM

[11] Runst, T., Sickel, W.: Sobolev Spaces of Fractional Order, Nemytskij Operators and Nonlinear Partial Differential Equations. de Gruyter Series in Nonlinear Analysis and Applications 3. Walter de Gruyter, Berlin (1996). | DOI | MR | JFM

[12] Triebel, H.: Theory of Function Spaces. Monographs in Mathematics 78. Birkhäuser, Basel (1983). | DOI | MR | JFM

[13] Triebel, H.: Theory of Function Spaces II. Monographs in Mathematics 84. Birkhäuser, Basel (1992). | DOI | MR | JFM

[14] Yang, D., Yuan, W.: New Besov-type spaces and Triebel-Lizorkin-type spaces including $Q$ spaces. Math. Z. 265 (2010), 451-480. | DOI | MR | JFM

[15] Yuan, W., Sickel, W., Yang, D.: Morrey and Campanato Meet Besov, Lizorkin and Triebel. Lecture Notes in Mathematics 2005. Springer, Berlin (2010). | DOI | MR | JFM

Cité par Sources :