| The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators |
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| 引用本文： | Jun Feng LI. The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators[J]. 数学学报(英文版), 2005, 21(6): 1495-1508. DOI: 10.1007/s10114-005-0560-2 |
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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(English Series), 2005, 21(6): 1495-1508. DOI: 10.1007/s10114-005-0560-2 |
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| Authors: | Jun Feng Li |
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| Affiliation: | (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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