Article
| Title: | Function algebras of Besov and Triebel-Lizorkin-type (English) |
| Author: | Bensaid, Fares |
| Author: | Moussai, Madani |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1281-1300 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | 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. (English) |
| Keyword: | Littlewood-Paley decomposition |
| Keyword: | Besov-type space |
| Keyword: | Triebel-Lizorkin-type space |
| MSC: | 42B25 |
| MSC: | 46E35 |
| DOI: | 10.21136/CMJ.2023.0585-22 |
| . | |
| Date available: | 2023-11-23T12:28:45Z |
| Last updated: | 2023-11-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151960 |
| . | |
| Reference: | [1] Bensaid, F., Moussai, M.: Realizations of the homogeneous Besov-type spaces.Methods Appl. Anal. 26 (2019), 349-370. Zbl 1455.46032, MR 4100094, 10.4310/maa.2019.v26.n4.a3 |
| Reference: | [2] Bergh, G., Löfström, J.: Interpolation Spaces: An Introduction.Grundlehren der mathematischen Wissenschaften 223. Springer, Berlin (1976). Zbl 0344.46071, MR 482275, 10.1007/978-3-642-66451-9 |
| Reference: | [3] Bourdaud, G., Moussai, M., Sickel, W.: Composition operators on Lizorkin-Triebel spaces.J. Funct. Anal. 259 (2010), 1098-1128. Zbl 1219.47092, MR 2652183, 10.1016/j.jfa.2010.04.008 |
| Reference: | [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. Zbl 1314.46038, MR 3262646, 10.1007/s10231-013-0342-x |
| Reference: | [5] Baraka, A. El: An embedding theorem for Campanato spaces.Electron. J. Differ. Equ. 66 (2002), Article ID 66, 17 pages. Zbl 1002.46024, MR 1921139 |
| Reference: | [6] Frazier, M., Jawerth, B.: Decomposition of Besov spaces.Indiana Univ. Math. J. 34 (1985), 777-799. Zbl 0551.46018, MR 808825, 10.1512/iumj.1985.34.34041 |
| Reference: | [7] Moussai, M.: Composition operators on Besov algebras.Rev. Mat. Iberoam. 28 (2012), 239-272. Zbl 1238.47040, MR 2904140, 10.4171/RMI/676 |
| Reference: | [8] Moussai, M.: Realizations of homogeneous Besov and Triebel-Lizorkin spaces and an application to pointwise multipliers.Anal. Appl., Singap. 13 (2015), 149-183. Zbl 1348.46039, MR 3319662, 10.1142/s0219530514500250 |
| Reference: | [9] Moussai, M.: Composition operators on Besov spaces in the limiting case $s=1+1/p$.Stud. Math. 241 (2018), 1-15. Zbl 1415.46024, MR 3732927, 10.4064/sm8136-4-2017 |
| Reference: | [10] Peetre, J.: New Thoughts on Besov Spaces.Duke University Mathematics Series I. Duke University, Durham (1976). Zbl 0356.46038, MR 0461123 |
| Reference: | [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). Zbl 0873.35001, MR 1419319, 10.1515/9783110812411 |
| Reference: | [12] Triebel, H.: Theory of Function Spaces.Monographs in Mathematics 78. Birkhäuser, Basel (1983). Zbl 0546.46027, MR 0781540, 10.1007/978-3-0346-0416-1 |
| Reference: | [13] Triebel, H.: Theory of Function Spaces II.Monographs in Mathematics 84. Birkhäuser, Basel (1992). Zbl 0763.46025, MR 1163193, 10.1007/978-3-0346-0419-2 |
| Reference: | [14] Yang, D., Yuan, W.: New Besov-type spaces and Triebel-Lizorkin-type spaces including $Q$ spaces.Math. Z. 265 (2010), 451-480. Zbl 1191.42011, MR 2609320, 10.1007/s00209-009-0524-9 |
| Reference: | [15] Yuan, W., Sickel, W., Yang, D.: Morrey and Campanato Meet Besov, Lizorkin and Triebel.Lecture Notes in Mathematics 2005. Springer, Berlin (2010). Zbl 1207.46002, MR 2683024, 10.1007/978-3-642-14606-0 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
