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国家自然科学基金(10601046)

作品数:5 被引量:14H指数:3
发文基金:国家自然科学基金更多>>
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Sharp L^2 Boundedness of the Oscillatory Hyper-Hilbert Transform along Curves被引量:7
2010年
Consider the oscillatory hyper-Hilbert transform Hn,α,βf(x)=∫0^1 f(x-Г(t))e^it-βt^-1-α dt along the curve P(t) = (tp1, tP2,..., tpn), where β 〉 α ≥ 0 and 0 〈 p1 〈 p2 〈 ... 〈 Pn. We prove that H n,α,β is bounded on L2 if and only if β ≥ (n + 1)α. Our work extends and improves some known results.
Jie Cheng CHENDa Shah FANXiang Rong ZHU
关键词:OSCILLATORY
A note on the Marcinkiewicz integral operators on F_p^(α,q)被引量:3
2007年
In this paper, we shall prove that the Marcinkiewicz integral operator #n, when its kernel Ω satisfies the L^1-Dini condition, is bounded on the Triehel-Lizorkin spaces. It is well known that the Triehel-Lizorkin spaces are generalizations of many familiar spaces such as the Lehesgue spaces and the Soholev spaces. Therefore, our result extends many known theorems on the Marcinkiewicz integral operator. Our method is to regard the Marcinkiewicz integral operator as a vector valued singular integral. We also use another characterization of the Triehel-Lizorkin space which makes our approach more clear.
ZHANG Chun-jieQIAN Rui-rui
The Existence of Weak Solutions to the 2D Euler Equations with Initial Vorticity in BMO
2007年
We shall prove that there exists a weak solution to the 2D Euler equations with initial vorticity in BMO and initial velocity in L^∞.
Xiang Rong ZHU
关键词:BMO
Some notes on a conjecture of Zygmund被引量:1
2008年
In this paper, some classes of differentiation basis are investigated and several positive answers to a conjecture of Zygmund on differentiation of integrals are presented.
CHEN Jie-cheng ZHANG Chun-jie
A New Class of Weights Adapted to Rough Singular Integrals and Marcinkiewicz Integrals被引量:3
2009年
In this paper, we introduce a new class of weights Ap (Rn) which retains many fine properties of the classical Muchenhoupt weights Ap (Rn). While Ap (Rn) is too big a class to obtain the weighted norm inequalities for rough singular integrals and Marcinkiewicz integrals, our new class Ap (Rn) adapts well to these rough operators. As applications, we improve some known weighted estimates.
Chun Jie ZHANGYing YOU
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