n 维 Hausdorff 算子的加权不等式
The Weighted Inequalities of n-Dimensional Hausdorff Operators
DOI: 10.12677/PM.2021.115093, PDF, HTML,    国家自然科学基金支持
作者: 周红秀：上海大学数学系, 上海
关键词: 算子；共轭 Hausdorff 算子；权函数；Hausdorff Operator； Adjoint Hausdorff Operator； Weight
摘要: 本文主要获得一些 n 维 Hausdorff 算子在加双权勒贝格函数空间中的有界性关于权函数的充要条件. 我们同时得到了 n 维共轭 Hausdorff 算子的加权不等式。
Abstract: In this paper, we obtain some necessary and sufficient conditions for the boundedness of the n-dimensional Hausdorff operators on the two-weighted Lebesgue spaces. The corresponding results for the adjoint of n-dimensional Hausdorff operators are also obtained.
文章引用：周红秀. n 维 Hausdorff 算子的加权不等式[J]. 理论数学, 2021, 11(5): 790-801. https://doi.org/10.12677/PM.2021.115093

参考文献

[1] Hausdorff, F. (1921) Summationsmethoden und Momentfolgen I. Mathematische Zeitschrift,9, 74-109. [Google Scholar] [CrossRef] 
[2] Hardy, G.H. (1925) Notes on Some Points in the Integral Calculus, LX. An Inequality between Integrals. Messenger of Mathematics, 54, 150-156.
[3] Hedberg L. (1972) On Certain Convolution Ineqalities. Proceedings of the American Mathe- matical Society, 36, 505-510. [Google Scholar] [CrossRef] 
[4] Siskakis, A.G. (1987) Composition Semigroups and the Ces`aro Operator on Hp. [Google Scholar] [CrossRef] 
[5] Georgakis, C. (1992) The Hausdorff Mean of a Fourier-Stieltjes Transform. Proceedings of the American Mathematical Society, 116, 465-471. [Google Scholar] [CrossRef] 
[6] Liflyand, E. and M´oricz, F. (2000) The Hausdorff Operator Is Bounded on the Real Hardy Space H1(R). Proceedings of the American Mathematical Society, 128, 1391-1396. [Google Scholar] [CrossRef] 
[7] Liflyand, E. and M´oricz, F. (2002) Commuting Relations for Hausdorff Opereators and Hilbert Transforms on Real Hardy Spaces. Acta Mathematica Hungarica, 97, 133-143. [Google Scholar] [CrossRef] 
[8] Kufner, A., Maligranda, L. and Persson, L.E. (2007) The Hardy Inequality: About Its History and Some Related Results. Vydavatelsky´ Servis, Uppsala University Library, Uppsala, 162 p.
[9] Andersen, K.F. (2003) Boundedness of Hausdorff Operators on Lp(Rn), H1(Rn) and BMO(Rn). Acta Scientiarum Mathematicarum, 69, 409-418.
[10] Kufner, A., Persson, L.E. and Samko, N. (2017) Weighted Inequalities of Hardy Type. 2nd Edition, World Scientific Publishing Company, Inc., River Edge, NJ, xx+459 p. [Google Scholar] [CrossRef] 
[11] Chen, J., Fan, D. and Wang, S. (2013) Hausdorff Operators on Euclidean Spaces. Applied Mathematics-A Journal of Chinese Universities, 28, 548-564. [Google Scholar] [CrossRef] 
[12] Liflyand, E. (2013) Hausdorff Operators on Hardy Spaces. Eurasian Mathematical Journal, 4, 101-141.
[13] Liflyand, E. (2018) Hardy Type Inequalities in the Category of Hausdorff Operators. In: Kara- petyants, A., Kravchenko, V. and Liflyand, E., Eds., Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics Statistics, Vol. 291, Springer, Cham, 81-91. [Google Scholar] [CrossRef] 

为你推荐