单边多线性极大算子在Campanato空间上的有界性
Boundedness of One-Sided Multilinear Maximal Operators on Campanato Spaces
摘要: 本文研究 Campanato空间上单边多线性极大算子的映射性质。利用Lebesgue空间上的有界性，证明了单边多线性Hardy-Littlewood极大算子和分数次极大算子是从单边Morrey空间到单边Campanato空间上有界的。
Abstract: This paper studies the mapping properties of one-sided multilinear maximal operators on Campanato spaces. Using the boundedness on Lebesgue spaces, we prove that the one-sided multilinear Hardy-Littlewood maximal operators and fractional maximal operators are bounded from one-sided Morrey spaces to one-sided Campanato spaces.
文章引用：李婷. 单边多线性极大算子在Campanato空间上的有界性[J]. 应用数学进展, 2024, 13(11): 5089-5099. https://doi.org/10.12677/AAM.2024.1311491

参考文献

[1] Sawyer, E. (1986) Weighted Inequalities for the One-Sided Hardy-Littlewood Maximal Func- tions. Transactions of the American Mathematical Society, 297, 53-61.
https://doi.org/10.1090/s0002-9947-1986-0849466-0
[2] Mart叫n-Reyes, F.J., Ortega Salvador, P. and de la Torre, A. (1990) Weighted Inequalities for One-Sided Maximal Functions. Transactions of the American Mathematical Society, 319, 517-534.
https://doi.org/10.1090/s0002-9947-1990-0986694-9
[3] Mart´ın-Reyes, F.J. and De La Torre, A. (1994) One-Sided BMO Spaces. Journal of the London Mathematical Society, 49, 529-542.
https://doi.org/10.1112/jlms/49.3.529
[4] Mart叫n-Reyes, F.J. and de la Torre, A. (1993) Two Weight Norm Inequalities for Fractional One-Sided Maximal Operators. Proceedings of the American Mathematical Society, 117, 483- 489.
https://doi.org/10.1090/s0002-9939-1993-1110548-9
[5] de Rosa, L. and Segovia, C. (2002) Equivalence of Norms in One-Sided Hp Spaces.Collectanea Mathematica, 53, 1-20.
[6] Hardy, G.H. and Littlewood, J.E. (1928) Some Properties of Fractional Integrals. I. Mathema- tische Zeitschrift, 27, 565-606.
https://doi.org/10.1007/bf01171116
[7] Kenig, C.E. and Stein, E.M. (1999) Multilinear Estimates and Fractional Integration. Mathe- matical Research Letters, 6, 1-15.
https://doi.org/10.4310/mrl.1999.v6.n1.a1
[8] Moen, K. (2009) Weighted Inequalities for Multilinear Fractional Integral Operators. Col- lectanea Mathematica, 60, 213-238.
https://doi.org/10.1007/bf03191210
[9] Ombrosi, S. and de Rosa, L. (2003) Boundedness of the Weyl Fractional Integral on One-Sided Weighted Lebesgue and Lipschitz Spaces. Publicacions Matem`atiques, 47, 71-102.
https://doi.org/10.5565/publmat 47103 04
[10] Imerlishvili, G. and Meskhi, A. (2022) Weighted Inequalities for One-Sided Multilinear Frac- tional Integrals. Positivity, 27, 1-21.
https://doi.org/10.1007/s11117-022-00954-6
[11] Lanzhe, L. (1998) Two Weight Inequalities for Fractional One-Sided Maximal Operators on Orlicz and Lorentz Spaces. Approximation Theory and Its Applications, 14, 28-37.
https://doi.org/10.1007/bf02836926
[12] Aimar, H. and Crescimbeni, R. (1998) On One-Sided BMO and Lipschitz Functions. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 27, 37-456.
[13] de Rosa, L. (2006) Two Weight Norm Inequalities for Fractional One-Sided Maximal and Integral Operators. Commentationes Mathematicae Universitatis Carolinae, 47, 35-46.
[14] Lorente, M. and Riveros, M.S. (2005) Weights for Commutators of the One-Sided Discrete Square Function, the Weyl Fractional Integral and Other One-Sided Operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 135, 845-862.
https://doi.org/10.1017/s0308210500004157
[15] 傅尊伟, 陆善镇. 单边Triebel-Lizorkin空间及其应用[J]. 中国科学: 数学, 2011, 41(1): 43-52.
[16] 赵凯, 张荣欣, 任晓芳. 极大算子交换子在各向异性Morrey-Herz空间上的有界性(英文) [J]. 应用数学, 2011, 24(1): 49-55.
[17] 朱诗红. 极大多线性Bochner-Riesz算子的Morrey空间有界性[J]. 应用数学学报, 2016, 39(1):153-160.
[18] 陶双平, 高荣. 多线性分数次积分和极大算子在Morrey空间上的加权估计[J]. 山东大学学报(理学版), 2018, 53(6): 30-37.
[19] Shi, S. and Fu, Z. (2013) Estimates of Some Operators on One-Sided Weighted Morrey Spaces. Abstract and Applied Analysis, 2013, 1-9.
https://doi.org/10.1155/2013/829218

为你推荐