Article
| Title: | The sharp constant for truncated Hardy-Littlewood maximal inequality (English) |
| Author: | Wu, Jia |
| Author: | Wei, Mingquan |
| Author: | Yan, Dunyan |
| Author: | Liu, Shao |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 549-565 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator $M^b_a$ and the strong truncated Hardy-Littlewood maximal operator $\widetilde {M}^{\boldsymbol {b}}_{\boldsymbol {a}}$, respectively. We first present the $L^1$-norm of $M^b_a$, and then the $L^1$-norm of $\widetilde {M}^{\boldsymbol {b}}_{\boldsymbol {a}}$ is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality. (English) |
| Keyword: | sharp constant |
| Keyword: | truncated maximal operator |
| Keyword: | strong maximal operator |
| MSC: | 42B25 |
| DOI: | 10.21136/CMJ.2025.0259-24 |
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| Date available: | 2025-05-20T11:46:47Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152957 |
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| Reference: | [1] Adams, D. R., Hedberg, L. I.: Function Spaces and Potential Theory.Grundlehren der Mathematischen Wissenschaften 314. Springer, Berlin (1996). Zbl 0834.46021, MR 1411441, 10.1007/978-3-662-03282-4 |
| Reference: | [2] Aldaz, J. M.: Remarks on the Hardy-Littlewood maximal function.Proc. R. Soc. Edinb., Sect. A, Math. 128 (1998), 1-9. Zbl 0892.42010, MR 1606325, 10.1017/S0308210500027116 |
| Reference: | [3] Aldaz, J. M., Lázaro, J. P.: The best constant for the centered maximal operator on radial decreasing functions.Math. Inequal. Appl. 14 (2011), 173-179. Zbl 1210.42031, MR 2796986, 10.7153/mia-14-14 |
| Reference: | [4] Aldaz, J. M., Lázaro, J. P.: On high dimensional maximal operators.Banach J. Math. Anal. 7 (2013), 225-243. Zbl 1266.42041, MR 3039949, 10.15352/bjma/1363784233 |
| Reference: | [5] Grafakos, L.: Classical Fourier Analysis.Graduate Texts in Mathematics 249. Springer, New York (2014). Zbl 1304.42001, MR 3243734, 10.1007/978-1-4939-1194-3 |
| Reference: | [6] Grafakos, L., Montgomery-Smith, S.: Best constants for uncentered maximal functions.Bull. Lond. Math. Soc. 29 (1997), 60-64. Zbl 0865.42020, MR 1416408, 10.1112/S0024609396002081 |
| Reference: | [7] Lu, S., Yan, D.: $L^p$ boundedness of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.Sci. China, Ser. A 45 (2002), 196-213. Zbl 1054.42013, MR 1893315, 10.1360/02ys9021 |
| Reference: | [8] Melas, A. D.: On the centered Hardy-Littlewood maximal operator.Trans. Am. Math. Soc. 354 (2002), 3263-3273. Zbl 1015.42015, MR 1897399, 10.1090/S0002-9947-02-02900-8 |
| Reference: | [9] Melas, A. D.: The best constant for the centered Hardy-Littlewood maximal inequality.Ann. Math. (2) 157 (2003), 647-688. Zbl 1055.42013, MR 1973058, 10.4007/annals.2003.157.647 |
| Reference: | [10] Soria, J., Tradacete, P.: Best constants for the Hardy-Littlewood maximal operator on finite graphs.J. Math. Anal. Appl. 436 (2016), 661-682. Zbl 1329.05286, MR 3446971, 10.1016/j.jmaa.2015.11.076 |
| Reference: | [11] Wei, M., Nie, X., Wu, D., Yan, D.: A note on Hardy-Littlewood maximal operators.J. Inequal. Appl. 2016 (2016), Article ID 21, 13 pages. Zbl 1333.42040, MR 3450806, 10.1186/s13660-016-0963-x |
| Reference: | [12] Zhang, X., Wei, M., Yan, D., He, Q.: Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces.Front. Math. China 15 (2020), 215-223 \99999DOI99999 10.1007/s11464-020-0812-6 . Zbl 1440.42073, MR 4074355, 10.1007/s11464-020-0812-6 |
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