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1.
The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p(R^n),P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p(R^n) into weak Lμ^p(R^n),1≤p〈∞. 相似文献
2.
Zhijian Wu 《Advances in Applied Clifford Algebras》1998,8(1):83-93
We decompose Lα2(ℝ+
n+1) into direct sum of closed subspaces which are isomorphic to the monogenic Bergman space. Application on commutators is also
discussed.
Research supported in part by the NSF Grant DMS-9622890 相似文献
3.
Zeng Jian LOU Shou Zhi YANG Dao Jin SONG 《数学学报(英文版)》2005,21(4):949-954
We give a decomposition of the Hardy space Hz^1(Ω) into "div-curl" quantities for Lipschitz domains in R^n. We also prove a decomposition of Hz^1(Ω) into Jacobians det Du, u ∈ W0^1,2 (Ω,R^2) for Ω in R^2. This partially answers a well-known open problem. 相似文献
4.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
5.
In this paper, it was proved that the commutator
generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L
p1 (ℝ
n
) to L
p2 (ℝ
n
) if and only if b is a CṀO(ℝ
n
) function, where 1/p
1 − 1/p
2 = β/n, 1 < p
1 < ∞, 0 ⩽ β < n. Furthermore, the characterization of
on the homogenous Herz space
(ℝ
n
) was obtained.
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10571014, 10371080) and
the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No. 20040027001) 相似文献
6.
In this paper, the boundedness of Toeplitz operator T
b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε
(ℝn) is discussed from L
p(ℝn) to L
q(ℝn),
, and from L
p(ℝn) to Triebel-Lizorkin space
. We also obtain the boundedness of generalized Toeplitz operator Θ
α0
b
from L
p(ℝn) to L
q(ℝn),
. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator
T
b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L
p(ℝn), 1 < p < ∞. 相似文献
7.
In this paper the authors give a new integral estimate of the Bessel function,which is an extension of Calder(?)n-Zygmund's result.As an application of this result,we prove that the parameterized Marcinkiewicz integralμ_Ω~p with variable kernels is of type (2,2),where the kernel functionΩdoes not have any smoothness on the unit sphere in R~n. 相似文献
8.
M. E. Dudkin 《Ukrainian Mathematical Journal》1998,50(6):888-900
We give a criterion of invariance and symmetry of the restriction of an arbitrary unbounded self-adjoint operator in the space
L
2(ℝn, dx) by using the introduced notion of support of an arbitrary vector and the notion of capacity of a subspace N ⊂ ℝn.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 781–791, June, 1998.
This work was partially supported by the Foundation for Fundamental Research of the Ministry of Science and Technology of
the Ukraine (grant No. 1/238 “Operator”). 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.
In this paper we study pseudo-Riemannian submanifolds in ℝ
n
+k/t
satisfying the condition Δx=Ax+B, whereA is an endomorphism of ℝ
n
+k/t
andB is a constant vector in ℝ
n
+k/t
. We give a characterization theorem whenA is a self-adjoint endomorphism. As for hypersurfaces we are able to obtain a classification theorem for any endomorphismA.
Supported by a FPI Grant, DGICYT, 1990.
Partially supported by a DGICYT Grant No. PS87-0115-C03-03. 相似文献
11.
In this paper, the authors give a characterization of the (L
p, λ
, L
q, λ
)-compactness for the Riesz potential commutator [b,I
α
]. More precisely, the authors prove that the commutator [b,I
α
] is a compact operator from the Morrey space L
p, λ
(ℝ
n
) to L
q, λ
(ℝ
n
) if and only if b ∈ VMO(ℝ
n
), the BMO-closure of .
The research was supported by NSF of China (Grant: 10571015, 10826046) and SRFDP of China (Grant: 20050027025). 相似文献
12.
E. L. Alexandrov 《Mathematical Notes》2000,67(6):679-685
Explicit formulas are derived for the spectral function of double multiplication operator containing a multiplicative evolution
inL
2(X, μ)-space and a convolution-type operator inL
2(ℝ
n
)-spaces. Symmetric convolution and multiplication operators are considered inL
2(X, μ) andL
2(ℝ
n
)-spaces.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 803–810, June, 2000. 相似文献
13.
Xingde Dai David R. Larson Darrin M. Speegle 《Journal of Fourier Analysis and Applications》1997,3(4):451-456
A congruency theorem is proven for an ordered pair of groups of homeomorphisms of a metric space satisfying an abstract dilation-translation
relationship. A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive
matrix dilations on L
2
(ℝ
n). Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the
Borel structure ofℝ
n.
The second author is supported in part by NSF Grant DMS-9401544.
The third author was a Graduate Research Assistant at Workshop in Linear Analysis and Probability, Texas A&M University. 相似文献
14.
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
15.
This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces. 相似文献
16.
A Besov Estimate for Multilinear Singular Integrals 总被引:3,自引:0,他引:3
Wengu Chen 《数学学报(英文版)》2000,16(4):613-626
Abstract
The main purpose of this paper is to prove a good λ inequality for a multilinear singular integral in ℝ
n
.
The research is supported by Beijing Education Commission Foundation and Beijing Natural Science Foundation (Project No. 1982005) 相似文献
17.
In this paper, the authors consider a class of maximal multilinear singular integral operators
and maximal multilinear oscillatory singular integral operators with standard Calderón–Zygmund
kernels, and obtain their boundedness on L
p
(ℝ
n
) for 1 < p < ∞.
Research supported by Professor Xu Yuesheng’s Research Grant in the program of "One hundred Distinguished
Young Scientists" of the Chinese Academy of Sciences 相似文献
18.
V. V. Makeev 《Journal of Mathematical Sciences》2007,140(4):551-557
Here are three samples of results. (1) Let m be a finite (absolutely) continuous mass distribution in ℝ2, and let ℓ = {ℓ1, ..., ℓ5 ⊂ ℝ2} be a quintuple of rays with common origin such that any two adjacent angles between them make a sum of at most π. Then an
affine image of ℓ subdivides m into five parts with any prescribed ratios.
(2) For each finite continuous mass distribution m in ℝn, there exist n mutually orthogonal hyperplanes any two of which quarter m.
(3) Let m and m′ be two finite continuous mass distributions in ℝRn with common center of symmetry O. Then there exist n hyperplanes through O any two of which quarter both m and m′. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 92–106. 相似文献
19.
20.
Hyun Jae Yoo 《Mathematische Zeitschrift》2006,252(1):27-48
We consider fermion (or determinantal) random point fields on Euclidean space ℝd. Given a bounded, translation invariant, and positive definite integral operator J on L2(ℝd), we introduce a determinantal interaction for a system of particles moving on ℝd as follows: the n points located at x1,· · ·,xn ∈ ℝd have the potential energy given by where j(x−y) is the integral kernel function of the operator J. We show that the Gibbsian specification for this interaction is well-defined. When J is of finite range in addition, and for d≥2 if the intensity is small enough, we show that the fermion random point field corresponding to the operator J(I+J)−1 is a Gibbs measure admitted to the specification. 相似文献