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| 1 | Explicit constants for Hardy’s inequality with power weight on n-dimensional product spaces显示文摘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. | WANG ShiMo LU ShanZhen YAN DunYan | 2012 | Science China Mathematics2012，55，12： | 12 |
| 2 | L^p( [0, 1])-characterizations of multi-knot piecewise linear spectral sequences显示文摘在那里存在其指数的部分是明智的线性功能叫了的多结片的 L 2([0,1]), 的新 orthonormal 基础的一个班光谱序列。在这篇论文,我们证明这些底组成底,然而并非无条件的底,为 L p ([0,1])with 1 <
p <
∞
, p≠2。另外,我们在 L p ,Carleson 狩猎定理在上几乎到处,与这些有关的集中, Littlewood-Paley 定理和泊松求和公式基于…… | LIAN Qiaofang CHENG Linfeng YAN Dunyan | 2006 | Progress in Natural Science:Materials International2006，16，7： | 3 |
| 3 | Sharp bounds for Hardy type operators on higher-dimensional product spaces显示文摘Abstract We investigate a class of fractional Hardy type operators Hβ2,β2,...βm defined on higher-dimensional product spaces R^n1×R^n2×...R^nm and use novel methods to obtain their sharp result due to S.M.Wang,S.Z.Lu,and D.Y.Yan. | Qianjun HE Xiang LI Dunyan YAN | 2018 | Frontiers of Mathematics in China2018，13，6： | 3 |
| 4 | WEIGHTED BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL HARDY OPERATORS WITH BESOV-LIPSCHITZ FUNCTIONS显示文摘In this paper,we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions.The main result is that this kind of commutator,denoted by Hb α,is bounded from L x γp (R +) to Lx δ q (R +) with the bound explicitly worked out. | Shimo Wang Dunyan Yan | 2012 | Analysis in Theory and Applications2012，28，1： | 2 |
| 5 | Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces显示文摘We will prove that for 1 | Xingsong ZHANG Mingquan WEI Dunyan YAN Qianjun HE | 2020 | Frontiers of Mathematics in China2020，15，1： | 2 |
| 6 | Sharp constants in the doubly weighted Hardy-Littlewood-Sobolev inequality显示文摘It is well known that the doubly weighted Hardy-Littlewood-Sobolev inequality is as follows,Z Rn Z Rn f(x)g(y)|x||x.y||y|dxdy6 B(p,q,,,,n)kfkLp(Rn)kgkLq(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 11. | WU Di SHI ZuoShunHua YAN DunYan | 2014 | Science China Mathematics2014，57，5： | 2 |
| 7 | Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality显示文摘Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we consider whole ranges of p and q, i.e., 0 < p ≤∞ and 0 < q ≤∞. | Zuoshunhua Shi Wu Di Dunyan Yan | 2014 | Analysis in Theory and Applications2014，30，2： | 1 |
| 8 | Endpoint Estimates for Hardy Operator's Conjugate Operator with Power Weight on n-Dimensional Space显示文摘In this paper, we establish two integral inequalities for Hardy operator's conjugate operator at the endpoint on n-dimensional space. The operator H n is bounded from L1 xα(Gn) to Lq xβ(Gn) with the bound explicitly worked out and the similar result holds forH n. | Xudong Nie Shimo Wang Dunyan Yan | 2013 | Analysis in Theory and Applications2013，29，3： | 1 |
| 9 | Double Hilbert transform on D(R2)显示文摘 | Xiaona CUI Rui WANG Dunyan YAN | 2013 | Frontiers of Mathematics in China2013，8，4： | 1 |
| 10 | Limiting Property of the Distribution Function of L^p Function at Endpoints显示文摘We consider the limiting property of the distribution function of L^p function at endpoints 0 and ∞ and prove that for λ > 0 the following two equations limλ→+∞λ~pm({x : |f(x)| > λ}) = 0, limλ→0+λ~pm({x : |f(x)| > λ}) = 0hold for f ∈ L^p(Rn) with 1 ≤ p < ∞. This result is naturally applied to many operators of type(p, q) as well. | Shaozhen XU Dunyan YAN | 2016 | Journal of Mathematical Research with Applications2016，36，2： | 1 |
| 11 | A restriction theorem for oscillatory integral operator with certain polynomial phase显示文摘我们认为摆动的不可分的操作员是\({T_{ \alpha , m }} f\left ( x \right )={ \smallint _{{ \mathbb { R }^ n }}}{ e ^ i } \left ({ x_1 ^{{ \alpha _1 }} y_1 ^ m + \cdots x_1 ^{{ \alpha _n }} y_n ^ m } \right ) f\left ( y \right )dy\)在功能 f 是 Schwartz 的地方,工作。在这份报纸,为这个操作员的 S n-1 上的限制定理被获得。而且,我们获得保证限制定理的有效性的一个必要条件。 | Shaozhen XU Dunyan YAN | 2017 | Frontiers of Mathematics in China2017，12，4： | 1 |
| 12 | Sharp Bound for the Generalized m-Linear n-Dimensional Hardy-Littlewood-Polya Operator显示文摘In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results. | Qianjun He Mingquan Wei Dunyan Yan | 2023 | Analysis in Theory and Applications2023，39，1： | 0 |
| 13 | Boundedness of the Multilinear Maximal Operator with the Hausdorff Content显示文摘In this paper,we establish the strong and weak boundedness of the multilinear maximal operator in the setting of the Choquet integral with respect to theαdimensional Hausdorff content.Our results cover Orobitg and Verdera’s results in[8]. | Shao Liu Qianjun He Dunyan Yan | 2023 | Analysis in Theory and Applications2023，39，1： | 0 |
| 14 | Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces显示文摘We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator. | XIE LinSen LAN JiaCheng LAN SenHua YAN DunYan | 2009 | Science China Mathematics2009，52，3： | 0 |
| 15 | Sharp L^p decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables显示文摘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. | Shaozhen Xu Dunyan Yan | 2019 | Science China Mathematics2019，62，4： | 0 |
| 16 | Sharp constants for a class of multilinear integral operators and some applications显示文摘We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator. | WU Di YAN DunYan | 2016 | Science China Mathematics2016，59，5： | 0 |
| 17 | A Remark on Multilinear Oscillatory Singular Integrals | Shanzhen Lu Dunyan Yan Department of Mathematics, Beijing Normal University, Beijing 100875. P. R. China | 2000 | Acta Mathematica Sinica,English Series2000，16，4： | 0 |
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