共查询到20条相似文献,搜索用时 15 毫秒
1.
Bao-quan Yuan 《应用数学学报(英文版)》2006,22(3):413-418
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let (u(x,t),b(x,t)) be smooth solutions in (0, T). It is shown that the solution (u(x, t), b(x, t)) can be extended beyond t = T if (u(x,t), b(x, t)) ∈ L^1 (0, T; BMO) or the vorticity (rot u(x, t), rot b(x, t)) ∈ L^1 (0, T; BMO) or the deformation (Def u(x, t), Def b(x, t)) ∈ L^1 (0, T; BMO). 相似文献
2.
Sharp inequalities between weight bounds from A
2-condition and the BMO norm or the distance from L
∞ in the BMO norm are obtained in the one dimensional case. 相似文献
3.
Hông Vân Lê 《Journal of Geometry》2006,84(1-2):83-93
In this note we prove that any smooth (C1 resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get positive
answers to Lauritzen’s question and Amari’s question on a realization of smooth (C1 resp.) statistical manifolds as finite dimensional statistical models. 相似文献
4.
Yasuhiro Gotoh 《Journal d'Analyse Mathématique》1998,75(1):67-84
Extending results of Staples and Smith-Stegenga, we characterize measurable subsets of a given domainD ⊃R
n on which BMO(D) functions areL
p
integrable or exponentially integrable. In particular, we characterize uniform domains by the integrability of BMO functions.
We also remark on the boundedness of domains satisfying a certain integrability condition for the quasihyperbolic metric. 相似文献
5.
The present paper is concerned with elliptic systems with BMO coefficients: div(Au)=divF, where A(x) is a positive definite matrix whose entries are in BMO and F is a given matrix field in L
p
. We show existence and uniqueness of the distributional solution of class W
1,p
, provided p is close to 2, depending on the BMO norm of A. This result is achieved using a refinement of a classical Theorem of Coifman Rochberg and Weiss about commutators with BMO functions. 相似文献
6.
We study boundedness properties of a class ofmultiparameter paraproducts on the dual space of the dyadic Hardy space H d 1 (T N ), the dyadic product BMO space BMO d (T N ). For this, we introduce a notion of logarithmic mean oscillation on the polydisc. We also obtain a result on the boundedness of iterated commutators on BMO [0, 1] N ). 相似文献
7.
Chunjie Zhang 《分析论及其应用》2011,27(3):278-287
In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved. 相似文献
8.
Doyoon Kim 《Potential Analysis》2010,33(1):17-46
Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a
11) are measurable in time and one spatial variable, and have small BMO (bounded mean oscillation) semi-norms as functions of
the other spatial variables. The coefficient a
11 is measurable in time and have a small BMO semi-norm in the spatial variables. The unique solvability of equations in the
whole space is established. Then this result is applied to solving Dirichlet and Neumann boundary value problems for parabolic
equations defined on a half-space or on a bounded domain. 相似文献
9.
Let dγ(x) ≡ π
−n/2
e
−|x|
2
dx for all x ∈ ℝ
n
be the Gauss measure on ℝ
n
. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators.
To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L
p
(γ) to L
p/(1−pβ)(γ), or from the Hardy space H
1(γ) of Mauceri and Meda to L
1/(1−β)(γ) or from L
1/β
(γ) to BMO(γ), where β ∈ (0, 1) and p ∈ (1, 1/β). 相似文献
10.
Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón–Zygmund theory. They need not be
bounded in the classical Hardy, BMO and even some L
p
spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy
and BMO spaces, and a John–Nirenberg inequality.
S. Hofmann was supported by the National Science Foundation. 相似文献
11.
Fengping Yao 《Mathematical Methods in the Applied Sciences》2011,34(13):1587-1593
In this paper, we obtain the global regularity estimates in Orlicz spaces for second‐order divergence elliptic and parabolic equations with BMO coefficients in the whole space. In fact, the global result can follow from the local estimates. As a corollary we obtain Lp‐type regularity estimates for such equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
In terms of continuous decomposition and choosing an appropriate BMO function, the authors obtain a sharp necessary condition
for L
p boundedness of the commutators generated by Bochner-Riesz operators below the critical index and BMO functions.
相似文献
13.
In this paper, we obtain Lipschitz and BMO norm inequalities for the composition G ∘ T of the homotopy operator T and Green’s operator G applied to differential forms. We also investigate the relationship among Lipschitz norm, BMO norm and L
s
norm. 相似文献
14.
J. Huisman 《Annali di Matematica Pura ed Applicata》2003,182(1):21-35
We show that there is a large class of non-special divisors of relatively small degree on a given real algebraic curve. If
the real algebraic curve has many real components, such a divisor gives rise to an embedding (birational embedding, resp.)
of the real algebraic curve into the real projective space ℙ
r
for r≥3 (r=2, resp.). We study these embeddings in quite some detail.
Received: October 17, 2001?Published online: February 20, 2003 相似文献
15.
Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures 总被引:4,自引:0,他引:4
A scale of BMO spaces appears naturally in product spaces corresponding to the different, yet equivalent, characterizations
of the class of functions of bounded mean oscillation in one variable. S.-Y. Chang and R. Fefferman characterized product
BMO, the dual of the (real) Hardy spaceH
Re
1
on product domains, in terms of Carleson measures. Here we describe two other BMO spaces, one contained in and the other
containing product BMO, in terms of Carleson measures and Hankel operators. Both of these spaces play a significant role in
harmonic analysis of the polydisk and in multivariable operator theory.
First author supported in part by a grant from the National Science Foundation. Second author supported in part by a grant
from the Department of Energy. 相似文献
16.
We prove boundedness of the Lusin's area operatorS
T
on the space BMO(R
n
). 相似文献
17.
We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form
operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these
two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO
Dirichlet problem implies L
p
solvability for all p>p
0. 相似文献
18.
We give a classification of all equivelar polyhedral maps on the torus. In particular, we classify all triangulations and quadrangulations of the torus admitting a vertex transitive automorphism group. These are precisely the ones which are quotients of the regular tessellations {3,6}, {6,3} or {4,4} by a pure translation group. An explicit formula for the number of combinatorial types of equivelar maps (polyhedral and non-polyhedral) with n vertices is obtained in terms of arithmetic functions in elementary number theory, such as the number of integer divisors of n. The asymptotic behaviour for n→∞ is also discussed, and an example is given for n such that the number of distinct equivelar triangulations of the torus with n vertices is larger than n itself. The numbers of regular and chiral maps are determined separately, as well as the ones for all other kinds of symmetry. Furthermore, arithmetic properties of the integers of type p2+pq+q2 (or p2+q2, resp.) can be interpreted and visualized by the hierarchy of covering maps between regular and chiral equivelar maps or type {3,6} (or {4,4}, resp.). 相似文献
19.
The Dirichlet irregularity of the origin which is a boundary point of a Zalcman domainR is shown to be sufficient but not necessary for the occurrence of the Myrberg phenomenonH
∞
(R) =H
∞
(R) o φ for a two-sheeted unlimited smooth covering surface~R ofR with projection mapφ. The importance of the uniqueness theorem in such a study of the Myrberg phenomenon is stressed. A condition under which
the Myrberg phenomenon fails for the covering surface (~R, R, φ) is also considered.
To complete the present work the first (second, resp.) named author was supported in part by Grant-in-Aid for Scientific Research,
No. 07640154 (07640196, 08640194, 09640180, 09640230, resp.), Japanese Ministry of Education, Science and Culture. 相似文献
20.
We obtain the global W
1,p
, 1 < p < ∞, estimate for the weak solution of an elliptic system with discontinuous coefficients in non-smooth domains without
using maximal function approach. It is assumed that the boundary of a bounded domain is well approximated by hyperplanes at
every point and at every scale, and that the tensor coefficients belong to BMO space with their BMO semi-norms sufficiently
small.
S.-S. Byun was supported in part by KRF-2006-C00034 and L. Wang was supported in part by NSF Grant 0701392. 相似文献