| Title:
|
Hausdorff operator on Morrey spaces and Campanato spaces (English) |
| Author:
|
Ruan, Jianmiao |
| Author:
|
Fan, Dashan |
| Author:
|
Li, Hongliang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
505-517 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013). (English) |
| Keyword:
|
Hausdorff operator |
| Keyword:
|
Morrey space |
| Keyword:
|
Campanato space |
| MSC:
|
42B30 |
| MSC:
|
42B35 |
| MSC:
|
46E30 |
| idZBL:
|
07217148 |
| idMR:
|
MR4111856 |
| DOI:
|
10.21136/CMJ.2019.0386-18 |
| . |
| Date available:
|
2020-06-17T12:35:57Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148242 |
| . |
| Reference:
|
[1] Chen, J., Fan, D., Li, J.: Hausdorff operators on function spaces.Chin. Ann. Math., Ser. B 33 (2012), 537-556. Zbl 1261.42036, MR 2996530, 10.1007/s11401-012-0724-1 |
| Reference:
|
[2] Chen, J., Fan, D., Wang, S.: Hausdorff operators on Euclidean spaces.Appl. Math., Ser. B (Engl. Ed.) 28 (2013), 548-564. Zbl 1299.42078, MR 3143905, 10.1007/s11766-013-3228-1 |
| Reference:
|
[3] Chen, J., Zhu, X.: Boundedness of multidimensional Hausdorff operators on $H^{1}(R^{n})$.J. Math. Anal. Appl. 409 (2014), 428-434. Zbl 1309.42026, MR 3095051, 10.1016/j.jmaa.2013.07.042 |
| Reference:
|
[4] Fefferman, C., Stein, E. M.: $H^p$ spaces of several variables.Acta Math. 129 (1972), 137-193. Zbl 0257.46078, MR 0447953, 10.1007/BF02392215 |
| Reference:
|
[5] Fu, Z., Grafakos, L., Lu, S., Zhao, F.: Sharp bounds for $m$-linear Hardy and Hilbert operators.Houston J. Math. 38 (2012), 225-244. Zbl 1248.42020, MR 2917283 |
| Reference:
|
[6] Lerner, A. K., Liflyand, E.: Multidimensional Hausdorff operators on the real Hardy space.J. Aust. Math. Soc. 83 (2007), 79-86. Zbl 1143.47023, MR 2378435, 10.1017/S1446788700036399 |
| Reference:
|
[7] Liflyand, E.: Open problems on Hausdorff operators.Complex Analysis and Potential Theory World Scientific, Hackensack (2007), 280-285. Zbl 1156.30002, MR 2368363, 10.1142/9789812778833_0030 |
| Reference:
|
[8] Liflyand, E.: Boundedness of multidimensional Hausdorff operators on $H^1({\mathbb R}^n)$.Acta Sci. Math. 74 (2008), 845-851. Zbl 1199.47155, MR 2487949 |
| Reference:
|
[9] Liflyand, E.: Hausdorff operators on Hardy spaces.Eurasian Math. J. 4 (2013), 101-141. Zbl 1328.47039, MR 3382905 |
| Reference:
|
[10] Liflyand, E., Miyachi, A.: Boundedness of the Hausdorff operators in $H^p$ spaces, $0<p<1$.Stud. Math. 194 (2009), 279-292. Zbl 1184.42002, MR 2539556, 10.4064/sm194-3-4 |
| Reference:
|
[11] Liflyand, E., Móricz, F.: The Hausdorff operator is bounded on the real Hardy space $H^1({\mathbb R})$.Proc. Am. Math. Soc. 128 (2000), 1391-1396. Zbl 0951.47038, MR 1641140, 10.1090/S0002-9939-99-05159-X |
| Reference:
|
[12] Liflyand, E., Móricz, F.: Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces.Acta Math. Hung. 97 (2002), 133-143. Zbl 1012.47011, MR 1932800, 10.1023/A:1020867130612 |
| Reference:
|
[13] Móricz, F.: Multivariate Hausdorff operators on the spaces $H^{1}({\mathbb R}^{n})$ and ${\rm BMO({\mathbb R}^{n})}$.Anal. Math. 31 (2005), 31-41. Zbl 1093.47036, MR 2145404, 10.1007/s10476-005-0003-4 |
| Reference:
|
[14] Ruan, J., Fan, D.: Hausdorff operators on the power weighted Hardy spaces.J. Math. Anal. Appl. 433 (2016), 31-48. Zbl 1331.42018, MR 3388780, 10.1016/j.jmaa.2015.07.062 |
| Reference:
|
[15] Ruan, J., Fan, D., Wu, Q.: Weighted Herz space estimates for Hausdorff operators on the Heisenberg group.Banach J. Math. Anal. 11 (2017), 513-535. Zbl 1370.42020, MR 3679894, 10.1215/17358787-2017-0004 |
| Reference:
|
[16] Weisz, F.: The boundedness of the Hausdorff operator on multi-dimensional Hardy spaces.Analysis, München 24 (2004), 183-195. Zbl 1071.47033, MR 2085955, 10.1524/anly.2004.24.14.183 |
| Reference:
|
[17] Xiao, J.: $L^{p}$ and BMO bounds of weighted Hardy-Littlewood averages.J. Math. Anal. Appl. 262 (2001), 660-666. Zbl 1009.42013, MR 1859331, 10.1006/jmaa.2001.7594 |
| . |
