共查询到20条相似文献,搜索用时 62 毫秒
1.
Xiaodong Wang 《Journal of Geometric Analysis》2008,18(1):272-284
Let (M
n
,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ
0 of its universal covering satisfies λ
0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.
The author was partially supported by NSF Grant 0505645. 相似文献
2.
Bao Quan YUAN 《数学学报(英文版)》2008,24(2):253-266
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^*,γ(R^n), with 1〈p〈∞and A = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space. 相似文献
3.
Fernando Giménez 《Israel Journal of Mathematics》1990,71(2):239-255
LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK
H≥4λ and antiholomorphic Ricci curvatureρ
A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C
P
n−1(λ) andM=C
P
n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.
Work partially supported by a DGICYT Grant No. PS87-0115-CO3-01. 相似文献
4.
Abstract. It is proved that the semilinear elliptic problem with zero boundary value 相似文献
5.
Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}(n = 1,2,...) be a sequence of complex numbers satisfying sup | arg(λn)| 〈 α 〈 π/2 and denote by M(∧) = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ(λ∈∧). Let α0(z) be a weight function defined on B. We obtain a completeness theorem for the system M(∧) in the Hilbert space L^2 [B, α0]. 相似文献
6.
We prove that the relationE
K
σ is Borel reducible to isomorphism and complemented biembeddability between subspaces ofc
0 orl
p with 1≤p<2. We also show that the relationE
K
σ ⊗=+ is Borel reducible to isomorphism, complemented biembeddability, and Lipschitz isomorphism between subspaces ofL
p for 1≤p<2.
This author was supported by FAPESP Grant 2002/09662-1. 相似文献
7.
S. Sylvia Chu K. C. S. Pillai 《Annals of the Institute of Statistical Mathematics》1979,31(1):185-205
Power studies of tests of equality of covariance matrices of twop-variate normal populations Σ1=Σ2 against two-sided alternatives have been made based on the following six criteria: 1) Roy's largest root, 2) Hotelling's
trace, 3) Pillai's trace, 4) Wilks' criterion, 5) Roy's largest-smallest roots and 6) modified likelihood ratio. A general
theorem has been proved establishing the local unbiasedness conditions connecting the two critical values for tests 1) to
5). Extensive unbiased power tabulations have been made forp=2, for various values ofn
1,n
2, λ1 and λ2 wheren
i
is the df of the SP matrix from theith sample and λ
i
is theith latent root of Σ1Σ
2
−1
(i=1,2). Further, comparisons of powers of tests 1) to 5) have been made with those of the modified likelihood ratio after obtaining
the exact distribution of the latter forn
2=2n
1 andp=2. Equal tail areas approach has also been used further to compute powers of tests 1) to 4) forp=2 for studying the bias. Again, a separate study has been made to compare the powers of the largest-smallest roots test with
its three biased approximate approaches as well as the largest root. Since the largest root test was observed to have some
advantage over the others, critical values were also obtained for this test in the unbiased as well as equal tail areas case
forp=3.
This research was supported by David Ross Grant from Purdue University.
S. Sylvia Chu is now with Northwestern University. 相似文献
8.
Dariusz Buraczewski Teresa Martinez José L. Torrea Roman Urban 《Journal d'Analyse Mathématique》2006,98(1):113-143
We define and investigate the Riesz transform associated with the differential operatorL
λ
f(θ)=−f"(θ)−2λ cot’θ. We prove that it can be defined as a principal value and that it is bounded onL
P
([0, π],dm
λ
(θ)),dm
λ(θ)=sin2λ θdθ, for every 1<p<∞ and of weak type (1,1). The same boundedness properties hold for the maximal operator of the truncated operators. The speed
of convergence of the truncated operators is measured in terms of the boundedness inL
P
(dm
λ
), 1<p<∞, and weak type (1,1) of the oscillation and ρ-variation associated to them. Also, a multiplier theorem is proved to get
the boundedness of the conjugate function studied by Muckenhoupt and Stein for 1<p<∞ as a corollary of the results for the Riesz transform. Moreover, we find a condition on the weightv which is necessary and sufficient for the existence of a weightu such that the Riesz transform is bounded fromL
P
(v dm
λ
) intoL
P
(u dm
λ
).
The authors were partially supported by RTN Harmonic Analysis and Related Problems contract HPRN-CT-2001-00273-HARP.
The first and fourth authors were supported in part by KBN grant 1-P93A 018 26.
The second and third authors were partially supported by BFM grant 2002-04013-C02-02. 相似文献
9.
Tamar Burak 《Israel Journal of Mathematics》1972,12(1):79-93
Let A be the closed unbounded operator inL
p(G) that is associated with an elliptic boundary value problem for a bounded domainG. We prove the existence of a spectral projectionE determined by the set Γ = {λ;θ
1≦argλ≦θ
2} and show thatAE is the infinitesimal generator of an analytic semigroup provided that the following conditions hold: 1<p<∞; the boundary
ϖΓ of Γ is contained in the resolvent setp(A) ofA;π/2≦θ<θ
2≦3π/2 ; and there exists a constantc such that (I)││(λ-A)-1││≦c/│λ│ for λ∈ϖΓ. The following consequence is obtained: Suppose that there exist constantsM andc such that λ∈p(A) and estimate (I) holds provided that |λ|≧M and Re λ=0. Then there exist bounded projectionE
− andE
+ such thatA is completely reduced by the direct sum decompositionL
p(G)=E−Lp (G) ⊕E+Lp (G) and each of the operatorsAE
− and—AE
+ is the infinitestimal generator of an analytic semigroup. 相似文献
10.
On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary 总被引:1,自引:0,他引:1
We consider nonnegative solutions of initial-boundary value problems for parabolic equationsu
t=uxx, ut=(um)xxand
(m>1) forx>0,t>0 with nonlinear boundary conditions−u
x=up,−(u
m)x=upand
forx=0,t>0, wherep>0. The initial function is assumed to be bounded, smooth and to have, in the latter two cases, compact support. We prove
that for each problem there exist positive critical valuesp
0,pc(withp
0<pc)such that forp∃(0,p
0],all solutions are global while forp∃(p0,pc] any solutionu≢0 blows up in a finite time and forp>p
csmall data solutions exist globally in time while large data solutions are nonglobal. We havep
c=2,p
c=m+1 andp
c=2m for each problem, whilep
0=1,p
0=1/2(m+1) andp
0=2m/(m+1) respectively.
This work was done during visits of the first author to Iowa State University and the Institute for Mathematics and its Applications
at the University of Minnesota. The second author was supported in part by NSF Grant DMS-9102210. 相似文献
11.
Let {Y
i
;−∞<i<∞} be a doubly infinite sequence of independent random elements taking values in a separable real Banach space and stochastically
dominated by a random variable X. Let {a
i
;−∞<i<∞} be an absolutely summable sequence of real numbers and set V
i
=∑
k=−∞∞
a
i+k
Y
i
,i≥1. In this paper, we derive that if
and E|X|
μ
log
ρ
|X|<0, for some μ (0<μ<2, μ≠1) and ρ>0 then
for all ε>0.
This work was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2006-353-C00006,
KRF-2006-251-C00026). 相似文献
12.
Extremal probabilities for Gaussian quadratic forms 总被引:1,自引:0,他引:1
Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf
Q
P(Q≤x)=P(χ2
n
/n≤x), where χ
n
2
is a chi-square distributed rv with n=n(x) degrees of freedom, n(x) is a non-increasing function of x, n=1 iff x>x(1)=1.5364…, n=2 iff x[x(2),x(1)], where x(2)=1.2989…, etc., n(x)≤rank(Q). A similar statement is not true for the supremum: if 1<x<2 and Z
1
,Z
2
are independent standard Gaussian rv's, then sup0≤λ≤1/2
P{λZ
1
2
+(1−λ)Z
2
2
≤x} is taken not at λ=0 or at λ=1/2 but at 0<λ=λ(x)<1/2, where λ(x) is a continuous, increasing function from λ(1)=0 to λ(2)=1/2, e.g. λ(1.5)=.15…. Applications of our theorems include asymptotic
quantiles of U and V-statistics, signal detection, and stochastic orderings of integrals of squared Gaussian processes.
Received: 24 June 2002 / Revised version: 26 January 2003
Published online: 15 April 2003
Research supported by NSA Grant MDA904-02-1-0091
Mathematics Subject Classification (2000): Primary 60E15, 60G15; Secondary 62G10 相似文献
13.
Roger J. Metzger Carlos A. Morales 《Bulletin of the Brazilian Mathematical Society》2006,37(1):89-101
Rovella proved the existence of measure-persistent attractors for flows exhibiting a unique singularity with three real eigenvalues
satisfying λ2 < λ3 < 0 < λ1 < −λ3 ([Ro]). In this paper we prove that most of them are in fact homoclinic classes.
*Partially supported by IMPA and CNPq.
**Partially supported by CNPq, FAPERJ and PRONEX/DYN-SYS. from Brazil. 相似文献
14.
The present paper is concerned withL
p-theory of the uniformly elliptic differential operator
inR
n with coefficients of vanishing mean oscillation. Recent estimates for the Riesz transform combined with Fredholm index theory
enable us to establish invertibility of the map L:W
-1,pRn→W
1,pRn, for every 1<p<∞. As a side benefit, we obtain the existence and uniqueness theorem for the equationL
u=μ with a signed measure in the right hand side. Within the framework of quasiconformal mappings we give a fairly general
method of constructing solutions to the homogeneous equationL
u=0.
The research of the first author was supported by NSF Grant DMS-9401104. The research of the second author was carried out
during his visit to Syracuse University and was supported by NSF Grant DMS-9401104 and by GNAFA-CNR Florence. 相似文献
15.
We characterize cardinalsκ such that 2λ = 2κ wheneverκ ≦λ < 2κ using ideals in small algebras of sets satisfying certain completeness and saturation conditions.
Research of this author was supported by an NSF Grant. 相似文献
16.
Tetsutaro Shibata 《Annali di Matematica Pura ed Applicata》2003,182(2):211-229
We consider the two-parameter nonlinear eigenvalue problem?−Δu = μu − λ(u + u
p
+ f(u)), u > 0 in Ω, u = 0 on ∂Ω,?where p>1 is a constant and μ,λ>0 are parameters. We establish the asymptotic formulas for the variational eigencurves λ=λ(μ,α) as
μ→∞, where α>0 is a normalizing parameter. We emphasize that the critical case from a viewpoint of the two-term asymptotics
of the eigencurve is p=3. Moreover, it is shown that p=5/3 is also a critical exponent from a view point of the three-term asymptotics when Ω is a ball or an annulus. This sort
of criticality for two-parameter problems seems to be new.
Received: February 9, 2002; in final form: April 3, 2002?Published online: April 14, 2003 相似文献
17.
Gustavo A. Fernández-Alcober Jon González-Sánchez Andrei Jaikin-Zapirain 《Israel Journal of Mathematics》2008,166(1):393-412
Let G be a pro-p group and let k ≥ 1. If γ
k(p−1) (G) ≤ γ
r
for some r and s such that k(p − 1) < r + s(p − 1), we prove that the exponent of Ωi(G) is at most p
i+k−1 for all i.
Supported by the Spanish Ministry of Science and Education, grant MTM2004-04665, partly with FEDER funds.
The first author is also supported by the University of the Basque Country, grant UPV05/99.
The second author is also supported by the Basque Government. 相似文献
18.
Sudhasree Gadam 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):209-220
We study the behaviour of the positive solutions to the Dirichlet problem IR
n
in the unit ball in IR
R
wherep<(N+2)/(N−2) ifN≥3 and λ varies over IR. For a special class of functionsg viz.,g(x)=u
0
p
(x) whereu
0 is the unique positive solution at λ=0, we prove that for certain λ’s nonradial solutions bifurcate from radially symmetric
positive solutions. WhenN=1, we obtain the complete bifurcation diagram for the positive solution curve. 相似文献
19.
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
20.
Mats Andersson 《Journal d'Analyse Mathématique》1996,68(1):39-58
LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. 相似文献