| 具有齐次核的奇异积分算子的范数及其应用 |
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| 引用本文： | 洪勇.具有齐次核的奇异积分算子的范数及其应用[J].吉首大学学报(自然科学版),2017,38(5):1. |
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| 作者姓名： | 洪勇 |
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| 作者单位： | （广东财经大学统计与数学学院,广东 广州 510320) |
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| 摘 要： | 设K(x,y)满足K(x,y)=K(y,x)和K(tx,ty)=tλK(x,y).定义奇异积分算子T，T(f)(y)=∫+∞0K(x,y)f(x)dx,y∈(0,+∞)，推导出获得算子T的范数的充分条件.利用这个结果,证明了一些新的积分不等式.
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| 关 键 词： | 对称齐次核 奇异积分算子 范数 有界算子 |
Norm of a Singular Integral Operator with Homogeneous Kernel and Its Application |
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| HONG Yong.Norm of a Singular Integral Operator with Homogeneous Kernel and Its Application[J].Journal of Jishou University(Natural Science Edition),2017,38(5):1. |
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| Authors: | HONG Yong |
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| Institution: | (College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China) |
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| Abstract: | Suppose K(x,y) satisfies K(x,y)=K(y,x) and K(tx,ty)=tλK(x,y).Define the singular integral operator T as T(f)(y)=∫+∞0K(x,y)f(x)dx,y∈(0,+∞).Sufficient conditions guaranteeing the norm of T are obtained.Some new integral inequalities are proved from these results. |
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| Keywords: | symmetric homogeneous kernel singular integral operator norm bounded operator |
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