共查询到20条相似文献,搜索用时 31 毫秒
1.
Some criterions in order thatl
1 embeds complementably inE
Φ(μ) and inL
Φ(μ) are given. It is also proved that every idealL inL
Φ(μ) such thatI
Φ(x/‖x‖Φ)=1 for anyxεL/{0} is contained inE
Φ(μ). 相似文献
2.
Thierry De Pauw 《Journal of Geometric Analysis》2002,12(1):29-61
A concentrated (ξ, m) almost monotone measure inR
n
is a Radon measure Φ satisfying the two following conditions: (1) Θ
m
(Φ,x)≥1 for every x ∈spt (Φ) and (2) for everyx ∈R
n
the ratioexp [ξ(r)]r−mΦ(B(x,r)) is increasing as a function of r>0. Here ξ is an increasing function such thatlim
r→0-ξ(r)=0. We prove that there is a relatively open dense setReg (Φ) ∋spt (Φ) such that at each x∈Reg(Φ) the support of Φ has the following regularity property: given ε>0 and λ>0 there is an m dimensional spaceW ⊂R
n
and a λ-Lipschitz function f from x+W into x+W‖ so that (100-ε)% ofspt(Φ) ∩B (x, r) coincides with the graph of f, at some scale r>0 depending on x, ε, and λ. 相似文献
3.
Let Γ be a regular curve and Lp(Γ),1<p<+∞, be the class of all complex-valued functions f defined on Γ which are such that |f|p is integrable in sense of Lebesgue. In this work, we define the kth p-Faber polynomial Fk.p(z), the kth p-Faber principle part ≈Fk.p(1/z) for Γ, and defined the nth p-Faber-Laurent rational function Rn,p(f, z) and p-generalized modulus of continuity Ωp of a function f of Lp(Γ). We investigate some properties of Fk.p(z) and ≈Fk.p(1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ωp in the mean of functions of Lp(Γ) by the rational functions Rn.p(.,z). 相似文献
4.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
5.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
6.
Robert S. Strichartz 《Journal of Geometric Analysis》1991,1(3):269-289
Let μ be a measure on ℝn that satisfies the estimate μ(B
r(x))≤cr
α for allx ∈ ℝn and allr ≤ 1 (B
r(x) denotes the ball of radius r centered atx. Let ϕ
j,k
(ɛ)
(x)=2
nj2ϕ(ɛ)(2
j
x-k) be a wavelet basis forj ∈ ℤ, κ ∈ ℤn, and ∈ ∈E, a finite set, and letP
j
(T)=Σɛ,k
<T,ϕ
j,k
(ɛ)
>ϕ
j,k
(ɛ)
denote the associated projection operators at levelj (T is a suitable measure or distribution). Iff ∈Ls
p(dμ) for 1 ≤p ≤ ∞, we show thatP
j(f dμ) ∈ Lp(dx) and ||P
j
(fdμ)||L
p(dx)≤c2
j((n-α)/p′))||f||L
p(dμ) for allj ≥ 0. We also obtain estimates for the limsup and liminf of ||P
j
(fdμ)||L
p(dx) under more restrictive hypotheses.
Communicated by Guido Weiss 相似文献
7.
V. V. Makeev 《Journal of Mathematical Sciences》2011,175(5):572-573
Let X be an affine cross-polytope, i.e., the convex hull of n segments A
1
B
1,…, A
n
B
n
in
\mathbbRn {\mathbb{R}^n} that have a common midpoint O and do not lie in a hyperplane. The affine flag F(X) of X is the chain O ∈ L
1 ⊂⋯ ⊂ L
n
=
\mathbbRn {\mathbb{R}^n} , where L
k
is the k-dimensional affine hull of the segments A
1
B
1,…, A
k
B
k
, k ≤ n. It is proved that each convex body K ⊂
\mathbbRn {\mathbb{R}^n} is circumscribed about an affine cross-polytope X such that the flag F(X) satisfies the following condition for each k ∈{2,…, n}:the (k−1)-planes of support at A
k
and B
k
to the body L
k
∩ K in the k-plane L
k
are parallel to L
k
−1.Each such X has volume at least V(K)/2
n(n−1)/2. Bibliography: 5 titles. 相似文献
8.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
9.
Jie-Cheng Chen 《Israel Journal of Mathematics》1993,81(1-2):193-202
In this paper, we get a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n, v(x)dx) to weak-L
Φ(R
+
n+1
,dμ), where Φ is anN-function satisfying the Δ2-condition. We also find a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n,v(x)dx) toL
Φ(R
+
n+1
,dμ) under some additional condition.
Partially supported by NNSF of P.R. China 相似文献
10.
We establish the equicontinuity and normality of the families R
Φ of ring Q(x)-homeomorphisms with integral-type restrictions ∫Φ(Q(x))dm(x) < ∞ on a domain D ⊂ R
n
with n ≥ 2. The resulting conditions on Φ are not only sufficient but also necessary for the equicontinuity and normality of these
families of mappings. We give some applications of these results to the Sobolev classes W
loc1,n
. 相似文献
11.
Quanhua Xu 《Israel Journal of Mathematics》1995,91(1-3):173-187
Let (Ω,F, P) be a probability space and {F
n}n≥0 a regular increasing sequence of sub-σ-fields ofF. LetH
1(Ω) be the usual Hardy space ofF
n-martingales. We show that the couple (H
1(Ω),L
∞(Ω)) is a partial retract of (L
1(Ω),L
∞(Ω)). It is also proved that (L
p(Ω),BMO(Ω)) is a partial retract of (L
p(Ω),L
∞(Ω)) for all 1<p<∞. 相似文献
12.
Pravin M. Vaidya 《Discrete and Computational Geometry》1991,6(1):369-381
A setV ofn points ink-dimensional space induces a complete weighted undirected graph as follows. The points are the vertices of this graph and
the weight of an edge between any two points is the distance between the points under someL
p metric. Let ε≤1 be an error parameter and letk be fixed. We show how to extract inO(n logn+ε
−k
log(1/ε)n) time a sparse subgraphG=(V, E) of the complete graph onV such that: (a) for any two pointsx, y inV, the length of the shortest path inG betweenx andy is at most (1+∈) times the distance betweenx andy, and (b)|E|=O(ε−k
n). 相似文献
13.
Jean-René Licois 《Journal d'Analyse Mathématique》1995,66(1):1-36
LetM be a compact riemannian manifold,h an odd function such thath(r)/r is non-decreasing with limit 0 at 0. Letf(r)=h(r)-γr and assume there exist non-negative constantsA andB and a realp>1 such thatf(r)>Ar
P-B. We prove that any non-negative solutionu ofu
tt+Δgu=f(u) onM x ℝ+ satisfying Dirichlet or Neumann boundary conditions on ϖM converges to a (stationary) solution of Δ
g
Φ=f(Φ) onM with exponential decay of ‖u-Φ‖C
2(M). For solutions with non-constant sign, we prove an homogenisation result for sufficiently small λ; further, we show that
for every λ the map (u(0,·),u
t(0,·))→(u(t,·), u
t(t,·)) defines a dynamical system onW
1/2(M)⊂C(M)×L
2(M) which possesses a compact maximal attractor.
相似文献
14.
1.IntroductionInthisarticleweconsiderthepointestimationofthegeneralizedprecisionofamultivariatenormaldistributionwithanunknownmeanvector.TObespecific,letXI,'?XubelidobservationfromNc(~,E)wherebothpERPandZ>0arecompletelyunknown.Insteadoftheoriginaldatasetonecanreducetheproblembysufficiencyandlookonlyatnn(X,S),whereX~n--1ZXiandS~Z(Xi--X)(Xi--X)'.ItiswellknownthatXisi=1i~1mutuallyindependentofSandX~Nc(~,n--'Z),S~Wb(n--1,Z).ThelossfunctionweconsiderinthispaperistheentropylossL(6,IZ… 相似文献
15.
Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let Ln(V) denote the nth homogeneous component of the free Lie algebra on V. We study the structure of Ln(V) as a module for the general linear group GLr(F) when n=pk and k is not divisible by p and where r≥n. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of
Lk(V) and the indecomposable direct summands of Ln(V) which are not isomorphic to direct summands of V⊗n. Our approach uses idempotents of the Solomon descent algebras, and in addition a correspondence theorem for permutation
modules of symmetric groups.
Second author supported by Deutsche Forschungsgemeinschaft (DFG-Scho 799). 相似文献
16.
James Olsen 《Israel Journal of Mathematics》1972,11(1):1-13
The principal result of this paper is that the convex combination of two positive, invertible, commuting isometries ofL
p(X,F, μ) 1<p<+∞, one of which is periodic, admits a dominated estimate with constantp/p−1. In establishing this, the following analogue of Linderholm’s theorem is obtained: Let σ and ε be two commuting non-singular
point transformations of a Lebesgue Space with τ periodic. Then given ε>O, there exists a periodic non-singular point transformation σ′ such that σ′ commutes with τ and μ(x:σ′x≠σx}<ε. Byan approximation argument, the principal result is applied to the convex combination of two isometries ofL
p (0, 1) induced by point transformations of the form τx=x
k,k>0 to show that such convex combinations admit a dominated estimate with constantp/p−1.
Research supported in part by NSF Grant No. GP-7475. A portion of the contents of this paper is based on the author’s doctoral
dissertation written under the direction of Professor R. V. Chacon of the University of Minnesota. 相似文献
17.
We prove inequalities about the quermassintegralsV
k
(K) of a convex bodyK in ℝ
n
(here,V
k
(K) is the mixed volumeV((K, k), (B
n
,n − k)) whereB
n
is the Euclidean unit ball). (i) The inequality
holds for every pair of convex bodiesK andL in ℝ
n
if and only ifk=2 ork=1. (ii) Let 0≤k≤p≤n. Then, for everyp-dimensional subspaceE of ℝ
n
,
whereP
E
K denotes the orthogonal projection ofK ontoE. The proof is based on a sharp upper estimate for the volume ratio |K|/|L| in terms ofV
n−k
(K)/V
n−k
(L), wheneverL andK are two convex bodies in ℝ
n
such thatK ⊆L. 相似文献
18.
LetA=(A
1,...,A
n
),B=(B
1,...,B
n
)εL(ℓ
p
)
n
be arbitraryn-tuples of bounded linear operators on (ℓ
p
), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators ε
a,b
on the Calkin algebraC(ℓ
p
)≡L(ℓ
p
)/K(ℓ
p
);
, where quotient elements are denoted bys=S+K(ℓ
p
) forSεL(ℓ
p
). It is shown among other results that the kernel Ker(ε
a,b
) is a non-separable subspace ofC(ℓ
p
) whenever ε
a,b
fails to be one-one, while the quotient
is non-separable whenever ε
a,b
fails to be onto. These results extend earlier ones in several directions: neither of the subsets {A
1,...,A
n
}, {B
1,...,B
n
} needs to consist of commuting operators, and the results apply to other spaces apart from Hilbert spaces.
Supported by the Academy of Finland, Project 32837. 相似文献
19.
Abraham Neyman 《Israel Journal of Mathematics》1984,48(2-3):129-138
For fixed 1≦p<∞ theL
p-semi-norms onR
n
are identified with positive linear functionals on the closed linear subspace ofC(R
n
) spanned by the functions |<ξ, ·>|
p
, ξ∈R
n
. For every positive linear functional σ, on that space, the function Φσ:R
n
→R given by Φσ is anL
p-semi-norm and the mapping σ→Φσ is 1-1 and onto. The closed linear span of |<ξ, ·>|
p
, ξ∈R
n
is the space of all even continuous functions that are homogeneous of degreep, ifp is not an even integer and is the space of all homogeneous polynomials of degreep whenp is an even integer. This representation is used to prove that there is no finite list of norm inequalities that characterizes
linear isometric embeddability, in anyL
p unlessp=2.
Supported by the National Science Foundation MCS-79-06634 at U.C. Berkeley. 相似文献
20.
P. Manselli 《Annali di Matematica Pura ed Applicata》2000,178(1):67-80
The subfamilyR(p, Ω) of the class of second order, uniformly elliptic, non variational operators L with bounded measurable coefficients,
such that L(W2, p (Ω)) is dense in Lp (Ω), is studied. Sufficient and necessary and sufficient conditions are given, for L to belong toR(p, Ω). An operator L of the class above and not inR(p, Ω) is constructed.
Entrata in Redazione il 5 ottobre 1998. 相似文献