Hardy-Littlewood极大算子在Wiener Amalgam空间中的有界性
The Boundedness of the Hardy-Littlewood Maximal Operators in Wiener Amalgam Spaces
DOI: 10.12677/PM.2023.135125, PDF, HTML, 下载: 178  浏览: 1,122  国家自然科学基金支持
作者: 吴育联, 孙小春*, 徐郜婷：西北师范大学，数学与统计学院，甘肃 兰州
关键词: Hardy-Littlewood极大算子；Lebesgue空间；Wiener Amalgam空间；Hardy-Littlewood Maximal Operator； Lebesgue Spaces； Wiener Amalgam Spaces
摘要: 本文应用Wiener amalgam 空间的嵌入关系，证明了 Hardy-Littlewood 极大算子 M 的W(FLp,Lq)有界性和Wiener amalgam 空间中的弱(1,1)性。
Abstract: Using the embedding relationship of Wiener amalgam spaces, we proved that the Hardy-Littlewood maximal operator M is bounded from W(FLp,Lq) to W(FLp,Lq). Meanwhile, we obtained that the Hardy-Littlewood maximal operator M is weak (1,1) in Wiener amalgam spaces.
文章引用：吴育联, 孙小春, 徐郜婷. Hardy-Littlewood极大算子在Wiener Amalgam空间中的有界性[J]. 理论数学, 2023, 13(5): 1219-1226. https://doi.org/10.12677/PM.2023.135125

参考文献

[1] Stein, E.M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 149-182.
[2] Kinnunen, J. (1997) The Hardy-Littlewood Maximal Function of a Sobolev Function. Israel Journal of Mathematics, 100, 117-124.
https://doi.org/10.1007/BF02773636
[3] Diening, L. (2004) Maximal Function on Generalized Lebesgue Spaces Lp(⋅). Mathematical Inequalities and Applications, 7, 245-253.
https://doi.org/10.7153/mia-07-27
[4] Bennett, C., DeVore, R.A. and Sharpley, R.C. (1981) Weak-L1 and BMO. Annals of Mathematics, 113, 601-611.
https://doi.org/10.2307/2006999
[5] Wiener, N. (1926) On the Representation of Functions by Trigonometrical Integrals. Mathematische Zeitschrift, 24, 575-616.
https://doi.org/10.1007/BF01216799
[6] Wiener, N. (1932) Tauberian Theorems. Annals of Mathematics, 33, 1-100.
https://doi.org/10.2307/1968102
[7] Wiener, N. (1988) The Fourier Integral and Certain of Its Applications (Cambridge Mathematical Library). Cambridge University Press, Cambridge.
[8] Feichtinger, H.G. (1983) Banach Convolution Algebras of Wiener Type. Colloquia Mathematica Societatis Janos Bolyai, 35, 509-524.
[9] Heil, C. (2003) An Introduction to Weighted Wiener Amalgams. In: Krishna, M., Radha, R. and Thangavelu, S., Eds., Wavelets and Their Applications, Allied Publishers, New Delhi, 183-216.
[10] Cordero, E., D'Elia, L. and Trapasso, S.I. (2019) Norm Estimates for Τ-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces. Journal of Mathematical Analysis and Applications, 471, 541-563.
https://doi.org/10.1016/j.jmaa.2018.10.090
[11] Wei, M.Q. and Yan, D.Y. (2018) The Boundedness of Two Classes of Oscillator Integral Operators on Mixed Norm Space. Advances in Mathematics (China), 47, 71-80.
[12] Cunanan, J. and Tsutsui, Y. (2016) Trace Operators on Wiener Amalgam Spaces. Journal of Function Spaces, 2016, Article ID: 1710260.
https://doi.org/10.1155/2016/1710260
[13] 丁勇. 现代分析基础[M].北京:北京师范大学出版社, 2008.

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