共查询到10条相似文献,搜索用时 140 毫秒
1.
Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
2.
Huo Xiong WU Shan Zhi YANG 《数学学报(英文版)》2008,24(2):177-184
This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given. 相似文献
3.
Lanzhe Liu 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(4):185-196
Sharp function inequalities for several vector-valued, multilinear singular integral operators with non-smooth kernels are
obtained. As an application, some weighted L
p
(p > 1) norm inequalities for vector-valued multilinear operators are derived. 相似文献
4.
In this paper, we introduce the fractional integral operator T of degree α of order m with respect to a dilation A for 0 < α < 1 and . First we establish the Hardy-Littlewood-Sobolev inequalities for T on anisotropic Hardy spaces associated with dilation A, which show that T is bounded from H
p
to H
q
, or from H
p
to L
q
, where 0 < p ≤ 1/(1 + α) and 1/q = 1/p − α. Then we give anisotropic Hardy spaces estimates for a class of multilinear operators formed by fractional integrals
or Calderón-Zygmund singular integrals. Finally, we apply the above results to give the boundedness of the commutators of
T and a BMO function.
Research supported by NSF of China (Grant: 10571015) and SRFDP of China (Grant: 20050027025). 相似文献
5.
It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the
product spaces
to the Hardy spacesH
r
, (ℝ
n
) and the weak Hardy spaceH
r,∞ (ℝ
n
. As an application of this result, the L
p
,(ℝ
n
) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.
Project supparted in part by the National Natural Science Foundation of Chind (Grant No. 19131080) of China and Doctoral Programme
Foundation of Institution of Higher Education (Grant No. 98002703) of China. 相似文献
6.
This paper is concerned with singular integral operators on product domains with rough kernels both along radial direction and on spherical surface.Some rather weaker size conditions,which imply the Lp-boundedness of such operators for certain fixed p(1 p ∞),are given. 相似文献
7.
Yulan Jiao 《分析论及其应用》2010,26(3):261-277
In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the Lp(Rn) (1 < p < ∞) boundedness and a weak type L log L estimate for the corresponding maximal operator. 相似文献
8.
We obtain sharp estimates for some multilinear commutators related to certain sublinear integral operators. These operators
include the Littlewood-Paley operator and Marcinkiewicz operator. As an application, we obtain weighted L
p
(p > 1) inequalities and an L log L-type estimate for multilinear commutators.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1419–1431, October, 2007. 相似文献
9.
Boundedness of Multilinear Operators in Herz-type Hardy Space 总被引:1,自引:0,他引:1
Let κ∈ℕ. We prove that the multilinear operators of finite sums of products of singular integrals on ℝn are bounded from HK
α1,p1
q1
(ℝn) ×···×HK
αk,pk
qk
(ℝn) into HK
α,p
q
(ℝn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments
satisfied by the multilinear operators are also necessary when αj≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals
of any orders.
Received September 6, 1999, Revised November 17, 1999, Accepted December 9, 1999 相似文献
10.
We consider singular integral operators of the form (a)Z
1L−1Z2, (b)Z
1Z2L−1, and (c)L
−1Z1Z2, whereZ
1 andZ
2 are nonzero right-invariant vector fields, andL is theL
2-closure of a canonical Laplacian. The operators (a) are shown to be bounded onL
p for allp∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for anyp∈[1, ∞).
Research supported by the Australian Research Council.
Research carried out as a National Research Fellow. 相似文献