共查询到20条相似文献,搜索用时 640 毫秒
1.
DunYanYAN GuoEnHU 《数学学报(英文版)》2005,21(1):209-214
In this paper, the authors discuss a class of multilinear singular integrals and obtain that the operators are bounded from H^1(R^n) to weak L^1(R^n). Using this result, we can directly prove a main theorem in [5]. 相似文献
2.
We show that the Fréchet-Sobolev spaces C(ℝ) ∩ L
p
(ℝ) and C
k
(ℝ) ∩ L
p
(ℝ) are not isomorphic for p ≠ 2 and k ∈ ℕ.
Research supported by the Italian MURST. 相似文献
3.
Piotr Hajłasz 《manuscripta mathematica》1996,91(1):61-72
We prove that functions with bounded deformationu: Ω → ℝn, Ω ⊂ ℝn, i.e., such mappings that the symmetric part of the gradient
is a measure, are approximately differentiable a.e. Then we generalize the result to a more general class of functions.
This research was carried out while the author stayed in the ICTP in Trieste in 1995. He wishes to thank the ICTP for the
hospitality. The author was partially supported by KBN grant no. 2-PO3A-034-08. 相似文献
4.
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
5.
In this paper we establish a discrete Calderón’s identity which converges in both L
q
(ℝ
n+m
) (1<q<∞) and Hardy space H
p
(ℝ
n
×ℝ
m
) (0<p≤1). Based on this identity, we derive a new atomic decomposition into (p,q)-atoms (1<q<∞) on H
p
(ℝ
n
×ℝ
m
) for 0<p≤1. As an application, we prove that an operator T, which is bounded on L
q
(ℝ
n+m
) for some 1<q<∞, is bounded from H
p
(ℝ
n
×ℝ
m
) to L
p
(ℝ
n+m
) if and only if T is bounded uniformly on all (p,q)-product atoms in L
p
(ℝ
n+m
). The similar result from H
p
(ℝ
n
×ℝ
m
) to H
p
(ℝ
n
×ℝ
m
) is also obtained. 相似文献
6.
WANG Meng CHEN Jiecheng & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(1):98-108
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition. 相似文献
7.
Vladimir Shpilrain 《Israel Journal of Mathematics》1995,91(1-3):307-316
LetE be a bounded Borel subset of ℝn,n≥2, of positive Lebesgue measure andP
E the corresponding ‘Pompeiu transform”. We prove thatP
E is injective onL
p(ℝn) if 1≤p≤2n/(n-1). We explore the connection between this problem and a Wiener-Tauberian type theorem for theM(n) action onL
q(ℝn) for various values ofq. We also take up the question of whenP
E is injective in caseE is of finite, positive measure, but is not necessarily a bounded set. Finally, we briefly look at these questions in the
contexts of symmetric spaces of compact and non-compact type. 相似文献
8.
We consider a natural class of stochastic processes taking values in the space of smoothly bounded domains in ℝ
n
with compact closure. These processes are generated by stochastic flows on ℝ
n
which are obtained as the solutions of stochastic differential equations on ℝ
n
. We establish an Ito formula for smooth domain functionals, applied to processes in this class.
Received: 2 March 2001 / Revised version: 10 January 2002 / Published online: 22 August 2002 相似文献
9.
A subgroup D of GL (n, ℝ) is said to be admissible if the semidirect product of D and ℝ
n
, considered as a subgroup of the affine group on ℝ
n
, admits wavelets ψ ∈ L2(ℝ
n
) satisfying a generalization of the Calderón reproducing, formula. This article provides a nearly complete characterization
of the admissible subgroups D. More precisely, if D is admissible, then the stability subgroup Dx for the transpose action of D on ℝ
n
must be compact for a. e. x. ∈ ℝ
n
; moreover, if Δ is the modular function of D, there must exist an a ∈ D such that |det a| ≠ Δ(a). Conversely, if the last condition holds and for a. e. x ∈ ℝ
n
there exists an ε > 0 for which the ε-stabilizer D
x
ε
is compact, then D is admissible. Numerous examples are given of both admissible and non-admissible groups. 相似文献
10.
M. V. Korobkov 《Siberian Mathematical Journal》2009,50(5):874-886
We find necessary and sufficient conditions for a curve in ℝ
m×n
to be the gradient range of a C
1-smooth function υ: Ω ⊂ ℝ
n
→ ℝ
m
. We show that this curve has tangents in a weak sense; these tangents are rank 1 matrices and their directions constitute
a function of bounded variation. We prove also that in this case v satisfies an analog of Sard’s theorem, while the level
sets of the gradient mapping ▿υ: Ω → ℝ
m×n
are hyperplanes. 相似文献
11.
Given α, 0 < α < n, and b ∈ BMO, we give sufficient conditions on weights for the commutator of the fractional integral operator, [b, I
α
], to satisfy weighted endpoint inequalities on ℝn and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on ℝn. 相似文献
12.
Michael Hutchings 《Journal of Geometric Analysis》1997,7(2):285-304
We show that the least area required to enclose two volumes in ℝn orS
n forn ≥ 3 is a strictly concave function of the two volumes. We deduce that minimal double bubbles in ℝn have no empty chambers, and we show that the enclosed regions are connected in some cases. We give consequences for the structure
of minimal double bubbles in ℝn. We also prove a general symmetry theorem for minimal enclosures ofm volumes in ℝn, based on an idea due to Brian White.
Supported in part by NSF DMS-9409166. 相似文献
13.
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
14.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
15.
Bixiang Wang 《Frontiers of Mathematics in China》2009,4(3):563-583
We study the long time behavior of solutions of the non-autonomous reaction-diffusion equation defined on the entire space
ℝ
n
when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established
in L
2(ℝ
n
) and H
1(ℝ
n
), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails
of solutions outside bounded domains.
相似文献
16.
Nahum Zobin 《Journal of Geometric Analysis》1999,9(3):491-511
Consider the Sobolev space W
∞
k
(Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions
from W
∞
k
(Ω) to the whole ℝ2 with preservation of class, i.e., surjectivity of the restriction operator W
∞
k
(ℝ2) → W
∞
k
(Ω). 相似文献
17.
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
18.
19.
ON MULTILINEAR COMMUTATORS OF Θ-TYPE CALDERóN-ZYGMUND OPERATORS 总被引:2,自引:1,他引:1
In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces. 相似文献
20.
Lower semicontinuity for polyconvex functionals of the form ∫Ω
g(detDu)dx with respect to sequences of functions fromW
1,n
(Ω;ℝ
n
) which converge inL
1 (Ωℝ
n
) and are uniformly bounded inW
1,n−1 (Ω;ℝ
n
), is proved. This was first established in [5] using results from [1] on Cartesian Currents. We give a simple direct proof
which does not involve currents. We also show how the method extends to prove natural, essentially optimal, generalizations
of these results.
Supported by MURST, Gruppo Nazionale 40%
Partially supported by Australian Research Council 相似文献