| 基为Lorentz锥的管状区域上复Hardy空间HP(0＜p≤1)中函数边值的Fourier变换 |
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| 引用本文： | 刘荣,邓冠铁.基为Lorentz锥的管状区域上复Hardy空间HP(0＜p≤1)中函数边值的Fourier变换[J].北京师范大学学报(自然科学版),2018,54(2):151-156. |
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| 作者姓名： | 刘荣 邓冠铁 |
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| 作者单位： | 北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,100875,北京;北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,100875,北京 |
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| 基金项目： | 国家自然科学基金资助项目(11271045) |
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| 摘 要： | 设Hp(TΓ)为n维复区域上的复Hardy空间,其中TΓ是基为Rn 正则开凸锥Γ 的管状区域.当p≥1时,Li利用函数边值的Fourier变换得到了函数在Hp(TΓ)中的充要条件,把经典的Paley-Wiener定理之一推广到了高维.当0
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| 关 键 词： | Hardy空间 Fourier变换 管状区域 Lorentz锥 |
| 收稿时间： | 2017-02-20 |
Fourier transform of Hardy spaces Hp on tubes over the Lorentz cones for 0＜p≤l |
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| LIU Rong,DENG Guantie.Fourier transform of Hardy spaces Hp on tubes over the Lorentz cones for 0＜p≤l[J].Journal of Beijing Normal University(Natural Science),2018,54(2):151-156. |
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| Authors: | LIU Rong DENG Guantie |
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| Institution: | School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems of Ministry of Education,100875,Beijing |
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| Abstract: | Let Hp (T(r)) be the complex Hardy space on n-dimensional complex domain, where T? is the tube domain over a regular convex open cone Γ() R". For 1≤p＜∞,Li showed the sufficient and necessary condition of a function to be in Hp (T(r)) by analyzing Fourier transform of its non-tangential boundary value, thus extended one of the classical Paley-Wiener theorems to higher dimension. Li also showed the characteristics of boundary values of functions in Hp (T(r)),where 0＜p≤l and Γ is the first octant of R",in distributional sense. The main purpose of this work is to further study the case that Γ is the Lorentz cone of Rn,and extend research of function characteristics in higher dimensional complex Hardy space. |
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