共查询到20条相似文献,搜索用时 31 毫秒
1.
Boundedness of Some Maximal Commutators in Hardy-type Spaces with Non-doubling Measures 总被引:1,自引:0,他引:1
Guo En HU Yan MENG Da Chun YANG 《数学学报(英文版)》2007,23(6):1129-1148
Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO(μ) functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO(μ) functions, of the Hardv soace H^I(μ) of Tolsa. 相似文献
2.
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H
1 (ℝ
n
× ℝ
m
) to the Lebesgue space L
1(ℝ
n
× ℝ
m
) and their commutators with Lipschitz functions from the Hardy space H
1 (ℝ
n
× ℝ
m
) to the Lebesgue space L
q
(ℝ
n
× ℝ
m
) for some q > 1. 相似文献
3.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained. 相似文献
4.
Jing-shi XU Department of Mathematics Hunan Normal University Changsha China 《中国科学A辑(英文版)》2007,50(3):361-376
The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RBMO(μ) functions of Tolsa with non-doubling measures is obtained, provided that‖μ‖=∞and multilinear singular integrals are bounded from L1(μ)×L1(μ)to L1/2,∞(μ). 相似文献
5.
This paper presents a weighted L
2 estimate with power weights for the maximal operator of commutators generated by compactly supported multipliers and Lipschitz
functions. As an application, we study the almost convergence of the commutators, which is generated by the Bochner-Riesz
means under the critical index and Lipschitz functions, for functions in L
p
(p ⩾ 2). 相似文献
6.
Guo-en HU~ Da-chun YANG~ 《中国科学A辑(英文版)》2007,50(11):1621-1641
Letμbe a nonnegative Radon measure on R~d which only satisfiesμ(B(x,r))≤C_0r~n for all x∈R~d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions. 相似文献
7.
Boundedness of commutators on Hardy type spaces 总被引:18,自引:0,他引:18
Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 <β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases. 相似文献
8.
Wen-ming Li Shan-zhen Lu Hui-xia Mo 《应用数学学报(英文版)》2007,23(1):113-122
Let[b,T]be the commutator generated by a Lipschitz function b ∈ Lip(β)(0<β<1)and multiplierT.The authors studied the boundedness of[b,T]on the Lebesgue spaces and Hardy spaces. 相似文献
9.
Marcinkiewicz Integrals with Non-Doubling Measures 总被引:2,自引:0,他引:2
Let μ be a positive Radon measure on
which may be non doubling. The only condition that μ must satisfy is μ(B(x, r)) ≤ Cr
n
for all
, r > 0 and some fixed constants C > 0 and n ∈ (0, d]. In this paper, we introduce the Marcinkiewicz integral related to a such measure with kernel satisfying some H?rmander-type
condition, and assume that it is bounded on L
2(μ). We then establish its boundedness, respectively, from the Lebesgue space L
1(μ) to the weak Lebesgue space L
1,∞(μ), from the Hardy space H
1(μ) to L
1(μ) and from the Lebesgue space L
∞(μ) to the space RBLO(μ). As a corollary, we obtain the boundedness of the Marcinkiewicz integral in the Lebesgue space L
p
(μ) with p ∈ (1,∞). Moreover, we establish the boundedness of the commutator generated by the RBMO(μ) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger H?rmander-type condition, respectively,
from L
p
(μ) with p ∈ (1,∞) to itself, from the space L log L(μ) to L
1,∞(μ) and from H
1(μ) to L
1,∞(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
The third (corresponding) author was supported by National Science Foundation for Distinguished Young Scholars (No. 10425106)
and NCET (No. 04-0142) of China. 相似文献
10.
Wei-yi SU~ 《中国科学A辑(英文版)》2007,50(7):1005-1014
The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m<(ln 2/ln 3). 相似文献
11.
We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie
group satisfy a smoothness dichotomy: Either μ
k
is singular to Lebesgue measure or μ
k
∈ L
2. The minimum k for which μ
k
∈ L
2 is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.
S. K. Gupta appreciates the hospitality of the Department of Pure Mathematics at the University of Waterloo where some of
this research was done. K. E. Hare was supported in part by NSERC. 相似文献
12.
We obtain characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of Calderón-Zygmund and fractional type operators in the context of the variable exponent Lebesgue spaces L p(?), where the symbols of the commutators belong to the Lipschitz spaces. A useful tool is a pointwise estimate involving the sharp maximal operator of the commutator and certain associated maximal operators, which is new even in the classical context. Some boundedness properties of the commutators between Lebesgue and Lipschitz spaces in the variable context are also proved. 相似文献
13.
Abstract
Let μ and ν be normal functions and let T
g
be the extended Cesàso operator in terms of the symbol g. In this paper, we will characterize those g so that T
g
is bounded (or compact) from mixed norm spaces H(p, q, μ) to H(p, q, ν) in the unit ball of C
n
. Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces.
Supported by the National Natural Science Foundation of China (No.10571049, 10471039), the Natural Science Foundation of Zhejiang
Province (No. M103085). 相似文献
14.
In general, Banach space-valued Riemann integrable functions defined on [0, 1] (equipped with the Lebesgue measure) need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X* is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31(2), 697-703 (2001)] that L^1[0, 1] has the weak Lebesgue property. 相似文献
15.
主要讨论了满足H(m)条件的奇异积分算子与Lipschitz函数的交换子在L~p和Hardy空间的有界性,并把这个结果应用于与薛定谔算子相关的Riesz变换. 相似文献
16.
Anders Björn 《Czechoslovak Mathematical Journal》2006,56(1):179-227
We develop a theory of removable singularities for the weighted Bergman space
, where μ is a Radon measure on ℂ. The set A is weakly removable for
, and strongly removable for
.
The general theory developed is in many ways similar to the theory of removable singularities for Hardy H
p
spaces, BMO and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible
properties, e.g. the union of two compact removable singularities needs not be removable.
In the case when weak and strong removability are the same for all sets, in particular if μ is absolutely continuous with respect to the Lebesgue measure m, we are able to say more than in the general case. In this case we obtain a Dolzhenko type result saying that a countable
union of compact removable singularities is removable.
When dμ = wdm and w is a Muckenhoupt A
p
weight, 1 < p < ∞, the removable singularities are characterized as the null sets of the weighted Sobolev space capacity with respect to
the dual exponent p′ = p/(p − 1) and the dual weight w′ = w
1/(1 − p). 相似文献
17.
Zhijian Wu 《Frontiers of Mathematics in China》2007,2(2):287-303
We characterize the symbol functions so that the associated commutators with symbol functions and the Hilbert transform are
bounded on Lipschitz space Λ
α
p
, where 1 < p < ∞ and 0 < α < 1/p. Properties of such symbols are also discussed.
相似文献
18.
The (L^p, Fp^β,∞)-Boundedness of Commutators of Multipliers 总被引:1,自引:0,他引:1
Pu ZHANG Jie Cheng CHEN 《数学学报(英文版)》2005,21(4):765-772
In this paper, we study the commutator generalized by a multiplier and a Lipschitz function. Under some assumptions, we establish the boundedness properties of it from L^P(R^n) into Fp^β,∞(R^n), the Triebel Lizorkin spaces. 相似文献
19.
Let μ be a positive Borel measure having support supp μ ⊂ [1, ∞) and satisfying the conditionf(t−1)−1dμ(t)<∞. In this paper we study the order of the uniform approximation of the function
on the disk |z|≤1 and on the closed interval [−1, 1] by means of the orthogonal projection of
on the set of rational functions of degreen. Moreover, the poles of the rational functions are chosen depending on the measure μ. For example, it is shown that if supp
μ is compact and does not contain 1, then this approximation method is of best order. But if supp μ=[1,a],a>1, the measure μ is absolutely continuous with respect to the Lebesgue measure, and
fort∈[1,a] and some α>0, then the order of such an approximation differs from the best only by
.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 362–368, March, 1999. 相似文献
20.
L. B. Beinenson 《Journal of Mathematical Sciences》2005,131(2):5445-5470
In this part of the paper, we investigate the structure of an arbitrary measure μ supported by a polyhedral cone C in R
d in the case where the decumulative distribution function gμ of the measure μ satisfies certain continuity conditions. If a face Γ of the cone C satisfies appropriate conditions, the
restriction μ|Γint of the measure μ to the interior part of Γ is proved to be absolutely continuous with respect to the Lebesgue measure λΓ on the face Γ. Besides, the density of the measure μ|Γint is expressed as the derivative of the function gμ multipied by a constant. This result was used in the first part of the paper to find the finite-dimensional distributions
of a monotone random field on a poset. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 307, 2004, pp. 5–56. 相似文献