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| Estimates of three classical summations on the spaces F_p~(α,q)(R~n)(0 < p ≤ 1) | |
| 引用本文： | GAO Gui-lian,;ZHONG Yong. Estimates of three classical summations on the spaces F_p~(α,q)(R~n)(0 < p ≤ 1)[J]. 高校应用数学学报(英文版), 2014, 29(3): 329-338. DOI: 10.1007/s11766-014-3141-2 |
| 作者姓名： | GAO Gui-lian, ZHONG Yong |
| 作者单位： | [1]School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; [2]Postdoctoral Programme of Economics and Management School of Wuhan University, Wuhan 430072, China; [3]Postdoctoral Programme of China Great Wall Asset Management Corporation, Beijing 100045, China |
| 基金项目： | Supported by the Zhejiang Postdoctoral Science Foundation of China （BSH1302046）, the National Natural Science Foundation of China （11271330） and the Zhejiang Natural Science Foundation of China （Y604563）. |
| 摘 要： | We obtain the boundedness on ˙Fα,qp(Rn) for the Poisson summation and Gauss summation. Their maximal operators are proved to be bounded from˙Fα,qp(Rn) to L∞(Rn).For the maximal operator of the Bochner-Riesz summation, we prove that it is bounded from˙Fα,qp(Rn) to Lpnn-pα,∞(Rn). |
| 关 键 词： | 求和 空间 估算 运营商 有界性 证明 高斯 |
Estimates of three classical summations on the spaces dot F_p^{alpha,q} (mathbb{R}^n )(0 < p leqslant 1) |
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| Gui-lian Gao,Yong Zhong. Estimates of three classical summations on the spaces dot F_p^{alpha,q} (mathbb{R}^n )(0 < p leqslant 1)[J]. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3): 329-338. DOI: 10.1007/s11766-014-3141-2 | |
| Authors: | Gui-lian Gao Yong Zhong |
| Affiliation: | 1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China 2. Postdoctoral Programme of Economics and Management School of Wuhan University, Wuhan, 430072, China 3. Postdoctoral Programme of China Great Wall Asset Management Corporation, Beijing, 100045, China |
| Abstract: | We obtain the boundedness on (dot F_p^{alpha ,q} (mathbb{R}^n )(0 < p leqslant 1)) for the Poisson summation and Gauss summation. Their maximal operators are proved to be bounded from (dot F_p^{alpha ,q} (mathbb{R}^n )(0 < p leqslant 1)) to (L^infty (mathbb{R}^n )) . For the maximal operator of the Bochner-Riesz summation, we prove that it is bounded from (dot F_p^{alpha ,q} (mathbb{R}^n )(0 < p leqslant 1)) to (L^{tfrac{{pn}} {{n - palpha }},infty } (mathbb{R}^n ) ) . |
| Keywords: | Poisson summation Gauss summation Bochner-Riesz summation Triebel-Lizorkin space. |
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