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Sharp L^p decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables

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Science China Mathematics 2019年第4期62卷 649-662页

作者： Shaozhen Xu dunyan yan School of Mathematical Sciences University of Chinese Academy of Sciences

In this paper, we obtain the L^p decay of oscillatory integral operators T_λ with certain homogeneous polynomial phase functions of degree d in(n + n)-dimensions; we require that d > 2 n. If d/(d-n) < p < d/n,the decay is sharp and the decay rate is related to the Newton distance. For p = d/n or d/(d-n), we obtain the almost sharp decay, where "almost" means that the decay contains a log(λ) term. For otherwise, the L^p decay of T_λ is also obtained but not sharp. Finally, we provide a counterexample to show that d/(d-n) p d/n is not necessary to guarantee the sharp decay.

关键词： oscillatory integral operators sharp L^p decay several variables Newton distance

A restriction theorem for oscillatory integral operator with certain polynomial phase

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Frontiers of Mathematics in China 2017年第4期12卷 967-980页

作者： Shaozhen XU dunyan yan School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049China

We consider the oscillatory integral operator Ta,mf（X） f（y）dy, where the function f is a Schwartz *** this paper, the restriction theorem on Sn-1 for this operator is obtained. Moreover, we obtain a necessary cond... 详细信息

关键词： Restriction theorem oscillatory integral operator L2 boundedness,optimal estimate necessary condition

Double Hilbert transform on D（R2）

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Frontiers of Mathematics in China 2013年第4期8卷 783-799页

作者： Xiaona CUI Rui WANG dunyan yan School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China Sch-oolof Mathematics Jilin University Changchun 130012 China

We introduce a space DHH =D（R2） H2H1D（R2）, where D（R2） is the testing function space whose functions are infinitely differentiable and have bounded support, and H2H1D（R2） is the space the double Hilbert transform acting on the testing function space. We prove that the double Hilbert transform is a homeomorphism from DHH onto itself.

关键词： Double Hilbert transform vanishing moments homeomorphism

Sharp bounds for Hardy type operators on higher-dimensional product spaces

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Frontiers of Mathematics in China 2018年第6期13卷 1341-1353页

作者： Qianjun HE Xiang LI dunyan yan School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049 China

We investigate a class of fractional Hardy type operators $${\mathscr{H}_{{\beta _1},{\beta _2}, \ldots ,{\beta _m}}}$$ ... 详细信息

We investigate a class of fractional Hardy type operators $${\mathscr{H}_{{\beta _1},{\beta _2}, \ldots ,{\beta _m}}}$$ defined on higher-dimensional product spaces $${\mathbb{R}^{{n_1}}} \times {\mathbb{R}^{{n_2}}} \times \cdots \times {\mathbb{R}^{{n_m}}}$$ and use novel methods to obtain their sharp bounds. In particular, we optimize the result due to S. M. Wang, S. Z. Lu, and D. Y. yan [Sci. China Math., 2012, 55(12): 2469–2480].

关键词： Hardy type operators power weight sharp bounds

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

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Frontiers of Mathematics in China 2020年第1期15卷 215-223页

作者： Xingsong ZHANG Mingquan WEI dunyan yan Qianjun HE School of Mathematics University of Chinese Academy of SciencesBeijing 100049China School of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China

We will prove that for 1 详细信息

We will prove that for 1

关键词： Hardy-Littlewood maximal function truncated Hardy-Littlewood maximal function Morrey norms weak Morrey norms

BOUNDEDNESS OF MULTILINEAR LITTLEWOOD-PALEY OPERATORS ON AMALGAM-CAMPANATO SPACES

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Acta Mathematica Scientia 2020年第1期40卷 272-292页

作者： Xiang LI Qianjun HE dunyan yan School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China

In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-***,norm inequalities o... 详细信息

关键词： multilinear Littlewood-Paley g-function multilinear g^*λ-function AmalgamCampanato spaces

Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality

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Science China Mathematics 2014年第5期57卷 963-970页

作者： WU Di SHI ZuoShunHua yan dunyan School of Mathematical Sciences University of Chinese Academy of Sciences

It is well known that the doubly weighted Hardy-Littlewood-Sobolev inequality is as follows,｜∫Rn ∫Rn f（x）g（y）/｜x｜^α｜x-y｜^λ｜y｜^β dxdy｜≤ B（p,q,α,λ,β ,n）｜｜f｜｜Lp（Rn）｜｜g｜｜Lq（Rn）.The main purpose of this paper is to give the sharp constants B（p,q,,,,n）for the above inequality for three cases：（i）p=1 and q=1;（ii）p=1 and 1q 6∞,or 1p 6∞and q=1;（iii）1p,q∞and 1p＋1q=*** addition,the explicit bounds can be obtained for the case 1p,q∞and 1/p＋1/q〉1.

关键词： best constants Hardy-Littlewood-Sobolev inequality Schur's lemma

Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces

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Science China Mathematics 2012年第12期55卷 2469-2480页

作者： WANG ShiMo LU ShanZhen yan dunyan School of Mathematics Science Heilongjiang University Haerbin 150080 China School of Mathematics Beijing Normal University Beijing 100875 China School of Mathematics Graduate University Chinese Academy of Sciences Beijing 100049 China

In this paper, Hardy operator H on n-dimensional product spaces G = (0, ∞)n and its adjoint operator H* are investigated. We use novel methods to obtain two main results. One is that we characterize the sufficient and necessary conditions for the operators H and H* being bounded from Lp(G, xα) to Lq(G, xβ), and the bounds of the operators H and H* are explicitly worked out. The other is that when 1 < p = q < +∞, norms of the operators H and H* are obtained.

关键词： n-dimensional Hardy operator Hausdorff-Young inequality power weight

BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES

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Acta Mathematica Scientia 2022年第3期42卷 1191-1208页

作者： Qianjun HE Xinfeng WU dunyan yan School of Applied Science Beijing Information Science and Technology UniversityBeijing 100192China Department of Mathematics China University Mining&Technology(Beijing)Beijing 100083China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey ***,we give an endpoint estimate for multilinear fractional integral *** an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.

关键词： Multilinear fractional integral L^(r′,α)-Höormander condition commutators BMO spaces Morrey spaces multilinear Fourier multiplier