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1.
Letp(1, ). In this paper, the authors investigate the uniformL
p
(
n
) in of the oscillatory singular integral operatorT
defined by
where , is a real analytic function or a real-C
function on
n
×
n
, C
0
(
n
×
n
) andk is a variable Calderón-Zygmund kernel. Moreover, the uniform boundedness in of the commutators generated byT
and BMO(
n
) functions onL
p
(
n
) is also obtained.The research is supported in part by the NNSF and the SEDF of China. 相似文献
2.
Shanzhen Lu 《中国科学A辑(英文版)》1999,42(10):1039-1046
A criterion on some boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderon-Zygmund standard kernel. Project supported by the National Natural Science Foundation of China (Grnat No. 19131080). 相似文献
3.
Letn2. The authors establish theL
2(
n
)-boundedness of singular integrals with variable rough Calderón-Zygmund kernels associated to surfaces satisfying some conditions.The research is supported in part by the NNSF and the SEDF of China. 相似文献
4.
5.
Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of f.With the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this paper.The almost everywhere convergence and norm convergence of the proposed estimators are established. 相似文献
6.
Positivity - Let T be a Calderón-Zygmund operator of type $$omega $$ with $$omega (t)$$ being nondecreasing and satisfying a kind of Dini’s type condition and let $$T_{vec {b}}$$ be... 相似文献
7.
Analytic capacity is associated with the Cauchy kernel 1/z and the L ∞-norm. For n?∈??, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$ , 1?≤?i?≤?2, $x=(x_1,x_2)\in{\mathbb R}^2$ . The main result of this paper states that the capacities associated with the vectorial kernel (K 1, K 2) are comparable to analytic capacity. 相似文献
8.
Paweł Głowacki 《Journal d'Analyse Mathématique》2017,131(1):337-365
We show that the subalgebra of convolution operators with Calderón-Zygmund kernels on a homogeneous group G is inverse-closed in the algebra of all bounded linear operators on the Hilbert space L 2(G). The main tool used is a symbolic calculus, where the convolution of distributions on the group is translated via the abelian Fourier transform into a “twisted product” of symbols on the dual to the Lie algebra g of G. 相似文献
9.
Let µ be a Radon measure on ? d which may be non-doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Cr n for all x∈? d , r > 0 and for some fixed 0 < n ≤ d. In this paper, under this assumption, we prove that θ-type Calderón-Zygmund operator which is bounded on L 2(µ) is also bounded from L ∞(µ) into RBMO(µ) and from H atb 1,∞ (µ) into L 1(µ). According to the interpolation theorem introduced by Tolsa, the L p (µ)-boundedness (1 < p < ∞) is established for θ-type Calderón-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type Calderón-Zygmund operator with RBMO(µ) function are bounded on L p (µ) (1 < p < ∞). 相似文献
10.
Under the assumption that μ is a non-doubling measure on ℝ
d
which only satisfies some growth condition, the authors prove that the maximal multilinear Calderón-Zygmund operator is bounded
from (μ) × … × (μ) into L
p
(μ) for any p
1, … p
m
∈ (1, ∞) and p with 1/p = 1/p
1 + … + 1/p
m
, and bounded from (μ) × … × (μ) into weak-
L
p
(μ) if there exists any p
i
= 1. Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear Calderón-Zygmund operator.
The second (corresponding) author is supported by Tianyuan Fund of China (No. 10626055) and National Natural Science Foundation
of China (No. 10701078). 相似文献
11.
Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces 总被引:2,自引:1,他引:1
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established. 相似文献
12.
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal function estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained. 相似文献
13.
Let μ be a nonnegative Radon measure on ? d which satisfies the polynomial growth condition that there exist positive constants C 0 and n ∈ (0, d ] such that, for all x ∈ ? d and r >0, μ (B (x , r ))≤C 0 r n , where B (x , r ) denotes the open ball centered at x and having radius r . In this paper, we show that, if μ (? d )<∞, then the boundedness of a Calderón-Zygmund operator T on L 2(μ ) is equivalent to that of T from the localized atomic Hardy space h 1(μ ) to L 1,∞(μ ) or from h 1(μ ) to L 1(μ ). 相似文献
14.
Fengping Yao 《Archiv der Mathematik》2009,92(2):137-146
In this paper we give a new proof for Lp estimates of the Calderón-Zygmund type singular integrals. Our approach is completely free from harmonic analysis.
This work was partially supported by the innovation foundation of Shanghai university under
Grant A10-0101-08-905. 相似文献
15.
CHEN Jiecheng DING Yong & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(5):639-650
In this paper we study a certain directional Hilbert transform and the bound-edness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems. 相似文献
16.
Andrei K. Lerner 《Journal d'Analyse Mathématique》2013,121(1):141-161
Given a general dyadic grid D and a sparse family of cubes S = {Q j k ∈ D, define a dyadic positive operator A D,S by $${A_{D,S}}f(x) = \sum\limits_{j,k} {{f_{Q_j^k}}{\chi _{Q_j^k}}} (x)$$ . Given a Banach function space X(? n ) and the maximal Calderón-Zygmund operator ${T_\natural }$ , we show that $${\left\| {{T_\natural}f} \right\|_X} \leqslant c(T,n)\mathop {\sup }\limits_{D,S} {\left\| {{A_{D,S}}|f|} \right\|_X}$$ This result is applied to weighted inequalities. In particular, it implies (i) the “twoweight conjecture” by D. Cruz-Uribe and C. Pérez in full generality; (ii) a simplification of the proof of the “A 2 conjecture”; (iii) an extension of certain mixed A p ?A r estimates to general Calderón-Zygmund operators; (iv) an extension of sharp A 1 estimates (known for T ) to the maximal Calderón-Zygmund operator $\natural $ . 相似文献
17.
Krzysztof Nowak 《Monatshefte für Mathematik》1993,116(1):49-72
We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane. 相似文献
18.
广义Calderón-Zygmund算子交换子的有界性 总被引:1,自引:0,他引:1
讨论了广义Calderón-Zyginund算子与Lipschitz函数生成的交换子在Lebe-sgue空间及Hardy空间上的有界性,同时得到了其端点估计. 相似文献
19.
Yan Lin 《数学学报(英文版)》2010,26(3):523-532
In this paper, the author states three classes of endpoint estimates for Calderon-Zygmund type operators. As their special cases, the corresponding results of classical Calderon-Zygmund operators can be deduced respectively. 相似文献
20.
本文讨论了δ-Calderon-Zygmund算子以及θ(t)-Calderon-Zygmund算子在Hardy型空间CHqp上的有界性. 相似文献