A class of multilinear oscillatory singular integrals related to block spaces

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概要

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• This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(R^n)$ boundedness of the multilinear oscillatory singular integral operators and that of the corresponding local multilinear singular integral operators are equivalent; and for any real-valued polynomial phase, the $L^p(R^n)$ boundedness of the multilinear oscillatory integral operators can be deduced from that of the corresponding multilinear singular integral operators.

• 東北大学の論文

著者

• LU Shanzhen

  Department of Mathematics Beijing Normal University

• Wu Huoxiong

  School of Mathematical Sciences, Xiamen University

• Wu Huoxiong

  School Of Mathematical Sciences Xiamen University

関連論文

• On a class of multilinear oscillatory singular integral operators
• Weighted L^p-boundedness for higher order commutators of oscillatory singular integrals
• A class of multilinear oscillatory singular integrals related to block spaces
• Criterion of (L^p, L^r) boundedness for a class of multilinear oscillatory singular integrals
• The commutator of the Bochner-Riesz operator
• Homogeneous fractional integrals on Hardy spaces
• A rough multiple Marcinkiewicz integral along continuous surfaces

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