共查询到20条相似文献,搜索用时 15 毫秒
1.
Elena Prestini 《数学学报(英文版)》2020,36(7):733-748
For double Walsh–Fourier series and with f ∈ L~2([0, 1) × [0, 1)) we prove two almost orthogonality results relative to the linearized maximal square partial sums operator S_(N(x,y))f(x, y).Assumptions are N(x, y) non-decreasing as a function of x and of y and, roughly speaking, partial derivatives with approximately constant ratio ■≌2~(n_0) for all x and y, where n_0 is any fixed non-negative integer. Estimates, independent of N(x, y) and n_0, are then extended to L~r, 1 r 2.We give an application to the family N(x, y) = λxy on [0, 1) × [0, 1), any λ 10. 相似文献
2.
Michael T. Lacey Xiaochun Li 《Transactions of the American Mathematical Society》2006,358(9):4099-4117
For a Schwartz function on the plane and a non-zero define the Hilbert transform of in the direction to be
p.v.
Let be a Schwartz function with frequency support in the annulus , and . We prove that the maximal operator maps into weak , and into for . The estimate is sharp. The method of proof is based upon techniques related to the pointwise convergence of Fourier series. Indeed, our main theorem implies this result on Fourier series. 3.
This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^* and TПb^* which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established. 相似文献
4.
The boundedness of commutators of multilinear singular integrals with Lipschitz functions in product Lebesgue spaces is obtained. 相似文献
5.
The boundedness of vector-valued multilinear commutators of singular integral operators whose kernels are variable with mixed homogeneity on Lebesgue spaces is obtained. 相似文献
6.
本文讨论了如下奇异积分算子:Tf(x)=P.V.∫R^nf(x-P(y))L(y)dy,其中P(y)=(p1(y),p2(y),…,pn(y)),K(y)=Ω(y)/‖y‖^n,∫S^n-1Ω(y)dσ(y)=0。对满足一定条件的P和Ω∈L^q(S^n-1)(q〉1),我们证明了T及其相应的极大奇异积分算子T^*都是L^p(R^n)上的有界算子。 相似文献
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In this article, we obtain the L p-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces. 相似文献
9.
Let μ be a nonnegative Radon measure on R d which satisfies the growth condition μ(B(x,r)) ≤ C0rn for all x ∈Rd and r >0,where C0 is a fixed constant and 0相似文献
10.
In this paper, we prove a multiple analog of the theorem proved by Arkhipov and the author in 1987, which provides an estimate for the discrete Hilbert transform with polynomial phase. For the linear case, the corresponding estimates of the sum of multiple trigonometric series was proved by Telyakovskii. 相似文献
11.
The quartile operator and pointwise convergence of Walsh series 总被引:3,自引:0,他引:3
Christoph Thiele 《Transactions of the American Mathematical Society》2000,352(12):5745-5766
The bilinear Hilbert transform is given by
It satisfies estimates of the type
In this paper we prove such estimates for a discrete model of the bilinear Hilbert transform involving the Walsh Fourier transform. We also reprove the well-known fact that the Walsh Fourier series of a function in , with converges pointwise almost everywhere. The purpose of this exposition is to clarify the connection between these two results and to present an easy approach to recent methods of time-frequency analysis.
12.
In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels. 相似文献
13.
I. A. Ikromov 《Mathematical Notes》2005,78(5-6):773-790
In the present paper, we consider estimates of the Fourier transform of Borel measures concentrated on analytic hypersurfaces and containing a mitigating factor. The mitigating factors are expressed in terms of principal curvatures of the surface. The resulting estimates are applied to investigating the boundedness of the corresponding maximal operators. 相似文献
14.
本文证明了与分数次积分和具有非光滑的奇异积分算子相关的Toeplitz型算子的sharp极大函数估计,做为应用,得到了该算子在Morrey空间的有界性. 相似文献
15.
Dashan Fan Kanghui Guo Yibiao Pan 《Transactions of the American Mathematical Society》2003,355(3):1145-1165
mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in .
16.
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of arbitrary shapes. 相似文献
17.
A. G. Lipchinskii 《Siberian Mathematical Journal》2005,46(4):652-660
We consider an interpolation process for the class of functions with finitely many singular points by means of the rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes constitute a triangular matrix and are distinct from the singular points of the function. We find a necessary and sufficient condition for uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence.Original Russian Text Copyright © 2005 Lipchinskii A. G.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 822–833, July–August, 2005. 相似文献
18.
Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type 下载免费PDF全文
Hung Viet Le 《分析论及其应用》2022,38(2):204-231
In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given. 相似文献
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LIU Feng WU Huo-xiong 《高校应用数学学报(英文版)》2014,29(1):86-100
In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1). 相似文献