| 变量核分数次积分在Hardy空间的有界性 |
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| 引用本文： | 张璞,丁勇.变量核分数次积分在Hardy空间的有界性[J].高校应用数学学报(英文版),2003,18(4):461-466. |
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| 作者姓名： | 张璞 丁勇 |
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| 作者单位： | Zhang Pu1 Ding Yong21 Dept.of Information and Computing Science，Zhejiang Institute of Science and Technology，Hangzhou 310033，China;Dept. of Math.，Zhejiang University，Hangzhou 310028，China. 2 Dept.of Math.，Beijing Normal University，Beijing 100875，China. |
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| 基金项目： | Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6) |
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| 摘 要： | § 1 Introduction and main resultsLet Sn- 1 be the unitsphere in Rn(n≥ 2 ) equipped with normalized Lebesgue measure dσ= dσ(z′) .We say that a functionΩ(x,z) defined on Rn× Rnbelongs to L∞ (Rn)× Lr(Sn- 1 )(r≥ 1 ) ,ifΩ(x,z) satisfies the following two conditions,(i) for any x,z∈Rnandλ>0 ,there hasΩ(x,λz) =Ω(x,z) ;(ii)‖Ω‖L∞(Rn)× Lr(Sn- 1) :=supx∈ Rn∫Sn- 1|Ω(x,z′) | rdσ(z′) 1 / r<∞ .For 0 <α
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| 收稿时间： | 6 June 2002 |
Fractional integrals with variable kernels on hardy spaces |
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| Zhang?Pu,Ding?Yong.Fractional integrals with variable kernels on hardy spaces[J].Applied Mathematics A Journal of Chinese Universities,2003,18(4):461-466. |
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| Authors: | Zhang Pu Ding Yong |
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| Institution: | (1) Dept. of Information and Computing Science, Zhejiang Institute of Science and Technology, 310033 Hangzhou, China;(2) Dept. of Math., Zhejiang University, 310028 Hangzhou, China;(3) Dept. of Math., Beijing Normal University, 100875 Beijing, China |
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| Abstract: | The fractional integral operators with variable kernels are discussed. It is proved that if the kernel satisfies the Dini-condition,
then the fractional integral operators with variable kernels are bounded from H
p (R
n
) into L
q (R
n
) when 0<p≤1 and 1/q=1/p−a/n. The results in this paper improve the results obtained by Ding, Chen and Fan in 2002.
Supported by the 973 Project (G1999075105) and the National Natural Science Foundation of China (10271016). |
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| Keywords: | fractional integral variable kernel Dini-condition Hardy space |
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