Article
| Title: | On the regularity of bilinear maximal operator (English) |
| Author: | Liu, Feng |
| Author: | Wang, Guoru |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 277-295 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | We study the regularity properties of bilinear maximal operator. Some new bounds and continuity for the above operators are established on the Sobolev spaces, Triebel-Lizorkin spaces and Besov spaces. In addition, the quasicontinuity and approximate differentiability of the bilinear maximal function are also obtained. (English) |
| Keyword: | bilinear maximal operator |
| Keyword: | Triebel-Lizorkin space |
| Keyword: | Besov space |
| Keyword: | Lipschitz space |
| Keyword: | $p$-quaiscontinuous |
| Keyword: | approximate differentiability |
| MSC: | 42B25 |
| MSC: | 46E35 |
| idZBL: | Zbl 07655768 |
| idMR: | MR4541102 |
| DOI: | 10.21136/CMJ.2022.0153-22 |
| . | |
| Date available: | 2023-02-03T11:15:24Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151517 |
| . | |
| Reference: | [1] Carneiro, E., Moreira, D.: On the regularity of maximal operators.Proc. Am. Math. Soc. 136 (2008), 4395-4404. Zbl 1157.42003, MR 2431055, 10.1090/S0002-9939-08-09515-4 |
| Reference: | [2] Federer, H., Ziemer, W. P.: The Lebesgue set of a function whose distribution derivatives are $p$-th power summable.Indiana Univ. Math. J. 22 (1972), 139-158. Zbl 0238.28015, MR 0435361, 10.1512/iumj.1972.22.22013 |
| Reference: | [3] Frazier, M., Jawerth, B., Weiss, G.: Littlewood-Paley Theory and The Study of Function Spaces.Regional Conference Series in Mathematics 79. AMS, Providence (1991). Zbl 0757.42006, MR 1107300, 10.1090/cbms/079 |
| Reference: | [4] Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order.Grundlehren der Mathematischen Wissenschaften 224. Springer, Berlin (1983). Zbl 0562.35001, MR 0737190, 10.1007/978-3-642-61798-0 |
| Reference: | [5] Grafakos, L.: Classical and Modern Fourier Analysis.Pearson, Upper Saddle River (2004). Zbl 1148.42001, MR 2449250 |
| Reference: | [6] Hajłasz, P., Malý, J.: On approximate differentiability of the maximal function.Proc. Am. Math. Soc. 138 (2010), 165-174. Zbl 1187.42016, MR 2550181, 10.1090/S0002-9939-09-09971-7 |
| Reference: | [7] Hajłasz, P., Onninen, J.: On boundedness of maximal functions in Sobolev spaces.Ann. Acad. Sci. Fenn., Math. 29 (2004), 167-176. Zbl 1059.46020, MR 2041705 |
| Reference: | [8] Kilpeläinen, T., Kinnunen, J., Martio, O.: Sobolev spaces with zero boundary values on metric spaces.Potential Anal. 12 (2000), 233-247. Zbl 0962.46021, MR 1752853, 10.1023/A:1008601220456 |
| Reference: | [9] Kinnunen, J.: The Hardy-Littlewood maximal function of a Sobolev function.Isr. J. Math. 100 (1997), 117-124. Zbl 0882.43003, MR 1469106, 10.1007/BF02773636 |
| Reference: | [10] Kinnunen, J., Lindqvist, P.: The derivative of the maximal function.J. Reine. Angew. Math. 503 (1998), 161-167. Zbl 0904.42015, MR 1650343, 10.1515/crll.1998.095 |
| Reference: | [11] Kinnunen, J., Saksman, E.: Regularity of the fractional maximal function.Bull. Lond. Math. Soc. 35 (2003), 529-535. Zbl 1021.42009, MR 1979008, 10.1112/S0024609303002017 |
| Reference: | [12] Korry, S.: Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces.Rev. Mat. Complut. 15 (2002), 401-416. Zbl 1033.42013, MR 1951818, 10.5209/rev_REMA.2002.v15.n2.16899 |
| Reference: | [13] Korry, S.: A class of bounded operators on Sobolev spaces.Arch. Math. 82 (2004), 40-50. Zbl 1061.46034, MR 2034469, 10.1007/s00013-003-0416-x |
| Reference: | [14] Lacey, M. T.: The bilinear maximal function map into $L^p$ for $2/3< p \leq 1$.Ann. Math. (2) 151 (2000), 35-57. Zbl 0967.47031, MR 1745019, 10.2307/121111 |
| Reference: | [15] Liu, F., Liu, S., Zhang, X.: Regularity properties of bilinear maximal function and its fractional variant.Result. Math. 75 (2020), Article ID 88, 29 pages. Zbl 1440.42086, MR 4105758, 10.1007/s00025-020-01215-2 |
| Reference: | [16] Liu, F., Wu, H.: On the regularity of the multisublinear maximal functions.Can. Math. Bull. 58 (2015), 808-817. Zbl 1330.42014, MR 3415670, 10.4153/CMB-2014-070-7 |
| Reference: | [17] Liu, F., Wu, H.: On the regularity of maximal operators supported by submanifolds.J. Math. Anal. Appl. 453 (2017), 144-158. Zbl 1404.42036, MR 3641765, 10.1016/j.jmaa.2017.03.058 |
| Reference: | [18] Luiro, H.: Continuity of the maximal operator in Sobolev spaces.Proc. Am. Math. Soc. 135 (2007), 243-251. Zbl 1136.42018, MR 2280193, 10.1090/S0002-9939-06-08455-3 |
| Reference: | [19] Luiro, H.: On the regularity of the Hardy-Littlewood maximal operator on subdomains of $\Bbb R^n$.Proc. Edinb. Math. Soc., II. Ser. 53 (2010), 211-237. Zbl 1183.42025, MR 2579688, 10.1017/S0013091507000867 |
| Reference: | [20] 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: | [21] Whitney, H.: On totally differentiable and smooth functions.Pac. J. Math. 1 (1951), 143-159. Zbl 0043.05803, MR 0043878, 10.2140/pjm.1951.1.143 |
| Reference: | [22] Yabuta, K.: Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces.Appl. Math., Ser. B (Engl. Ed.) 30 (2015), 418-446. Zbl 1349.42037, MR 3434042, 10.1007/s11766-015-3358-8 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
