| The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators |
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| 作者姓名： | Jun Feng LI |
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| 作者单位： | Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| 摘 要： | In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A belong to L^p（R^n） for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are （L^p, L^p）-type operators for 1 〈 p 〈 ∞.
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| 关 键 词： | 多线性算子 Lipschitz函数 积分算子 数学分析 |
| 收稿时间： | 2004-08-18 |
| 修稿时间： | 2004-08-182004-08-25 |
The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators |
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| Jun Feng LI.The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators[J].Acta Mathematica Sinica,2005,21(6):1495-1508. |
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| Authors: | Jun Feng Li |
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| Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | In this paper, the author obtains that the multilinear operators of strongly singular integral
operators and their dual operators are bounded from some L
p
(ℝ
n
) to L
q
(ℝ
n
) when the m–th order
derivatives of A belong to L
r
(ℝ
n
) for r large enough. By this result, the author gets the estimates for
the Sharp maximal functions of the multilinear operators with the m–th order derivatives of A being
Lipschitz functions. It follows that the multilinear operators are (L
p
, L
p
)–type operators for 1 < p < ∞. |
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| Keywords: | Multilinear operators Lipschitz functions L p (ℝ n ) |
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