共查询到20条相似文献,搜索用时 31 毫秒
1.
Toshinori Sakai 《Graphs and Combinatorics》2002,18(1):169-192
Let n≥2 be an integer and let μ1 and μ2 be measures in ℝ2 such that each μ
i
is absolutely continuous with respect to the Lebesgue measure and μ1(ℝ2)=μ2(ℝ2)=n. Let u≠0 be a vector on the plane. We show that if μ1(B)=μ2(B)=n for some bounded domain B, then there exist positive integers n
1,n
2 with n
1+n
2=n and disjoint open half-planes D
1,D
2 such that , μ1(D
1)=μ2(D
1)=n
1 and μ1(D
2)=μ2(D
2)=n
2; or there exist positive integers n
1,n
2,n
3 with n
1+n
2+n
3=n and disjoint open convex domains D
1,D
2,D
3 such that , μ1(D
1)=μ2(D
1)=n
1, μ1(D
2)= μ2(D
2)=n
2, μ1(D
3)=μ2(D
3)=n
3 and such that the ray is parallel to u. We also show a similar result for partitioning of point sets on the plane.
Received: November 24, 1999 Final version received: February 9, 2001 相似文献
2.
Éric Amar 《Arkiv f?r Matematik》2000,38(1):1-20
LetB be the unit ball ofC
n
, I give necessary conditions on sequenceS of points inB to beH
∞(B) interpolating in term of aC
n
valued holomorphic function zero onS (a substitute for the interpolating Blaschke product).
These conditions are sufficient to prove that the sequenceS is interpolating for ∩
p>1
(B) and is also interpolating forH
p
(B) for 1≤p<∞. 相似文献
3.
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
4.
Intersection theorems with geometric consequences 总被引:3,自引:0,他引:3
In this paper we prove that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℱ we have |F ∩F′| ≡ μi (modp) for somei, 1 ≦i≦s, then |ℱ|≦(
s
n
).
As a consequence we show that ifR
n
is covered bym sets withm<(1+o(1)) (1.2)
n
then there is one set within which all the distances are realised.
It is left open whether the same conclusion holds for compositep. 相似文献
5.
In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted byB
π, p
(R
n
), 1≤p<∞, i.e., for 1<p<∞,B
π, p
(R
n
) is isomorphic tol
p
(Z
n
), and forp=1,B
π, 1
(R
n
) is isomorphic to the discrete Hardy space with several variables, which is denoted byH(Z
n
).
This project is supported by the National Natural Science Foundation of China (19671012) and Doctoral Programme Institution
of Higher Education Foundation of Chinese Educational Committee and supported by Youth Foundation of Sichuan. 相似文献
6.
This paper considers some random processes of the form X
n+1=T
X
n
+B
n
(mod p) where B
n
and X
n
are random variables over (ℤ/pℤ)
d
and T is a fixed d×d integer matrix which is invertible over the complex numbers. For a particular distribution for B
n
, this paper improves results of Asci to show that if T has no complex eigenvalues of length 1, then for integers p relatively prime to det (T), order (log p)2 steps suffice to make X
n
close to uniformly distributed where X
0 is the zero vector. This paper also shows that if T has a complex eigenvalue which is a root of unity, then order p
b
steps are needed for X
n
to get close to uniformly distributed for some positive value b≤2 which may depend on T and X
0 is the zero vector. 相似文献
7.
In the paper, the interpolation properties of the spacesH
p
s
(v; ℝ
n
) of Sobolev-Liouville type and the spacesB
p, q
s
(μ ℝ
n
) of Nikol'skii-Besov type generated by functions of polynomial growth that are infinitely differentiable outside of the origin
are studied. Interpolation formulas for the pairs {H(v
o
),H(v
1)} and {B(μ0),B(μ1)} of spaces of the above types for which the anisotropies of the interpolated spaces do not depend on each other are proved.
The investigated spaces, for certain specification of the generating functions, coincide with the classical (isotropic and
anisotropic) Sobolev-Liouville and Nikol'skii-Besov spaces.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 666–672, November, 1997.
Translated by A. I. Shtern 相似文献
8.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
9.
We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C
n
. The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C
n
such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least
where C
n
> 1 is a constant depending on n only, and as n→∞.
Received June 24, 1998, Accepted January 14, 1999 相似文献
10.
E. S. Dubtsov 《Siberian Mathematical Journal》2009,50(6):998-1006
Denote by Hol(B
n
) the space of all holomorphic functions in the unit ball B
n
of ℂ
n
, n ≥ 1. Given g ∈ Hol(B
m
) and a holomorphic mapping φ: B
m
→ B
n
, put C
φ
g
f = g · (f ∘ φ) for f ∈ Hol(B
n
). We characterize those g and φ for which C
φ
g
is a bounded (or compact) operator from the growth space A
−log(B
n
) or A
−β
(B
n
), β > 0, to the weighted Bergman space A
α
p
(B
m
), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators. 相似文献
11.
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
12.
We study the boundedness of the H
∞ functional calculus for differential operators acting in L
p
(R
n
; C
N
). For constant coefficients, we give simple conditions on the symbols implying such boundedness. For non-constant coefficients,
we extend our recent results for the L
p
theory of the Kato square root problem to the more general framework of Hodge-Dirac operators with variable coefficients
Π
B
as treated in L
2(R
n
; C
N
) by Axelsson, Keith, and McIntosh. We obtain a characterization of the property that Π
B
has a bounded H
∞ functional calculus, in terms of randomized boundedness conditions of its resolvent. This allows us to deduce stability under
small perturbations of this functional calculus. 相似文献
13.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
14.
J. Bourgain 《Israel Journal of Mathematics》1989,67(3):291-311
This paper is a follow up of [B1]. It is shown that the sequence of squares {n
2|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic method developed in [B1] and a precise estimate of the Λ(p)-constant for the sequence of squares itself. Analogues of this phenomenon are obtained for other arithmetic sets, such as
the sequence ofkth powers {n
k |n=1, 2, ...} or the sequence of prime numbers. Sections 2 and 3 of the paper are of independent interest to orthogonal system
theory. 相似文献
15.
Elena Rubei 《Annali dell'Universita di Ferrara》2004,50(1):151-165
This paper deals with syzygies of the ideals of the Veronese embeddings. By Green’s Theorem we know thatO
P
n
(d) satisfies Green-Lazarsfeld’s PropertyN
p ∀d≥p, ∀n. By Ottaviani-Paoletti’s theorem ifn≥2, d≥3 and 3d−2≤p thenO
P
n
(d) does not satisfy PropertyN
p. The casesn≥3, d≥3, d<p<3d−2 are still open (exceptn=d=3). Here we deal with one of these cases, namely we prove thatO
P
n
(3) satisfies PropertyN
4 ∀n. Besides we prove thatO
P
n
(d) satisfiesN
p ∀n≥p iffO
P
n
(d) satisfiesN
p.
Sunto L’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheO P n (d) soddisfa la proprietàN p di Green-Lazarsfeld ∀d≥p, ∀n. Per il teorema di Ottaviani-Paoletti sen≥2, d≥3 and 3d−2≤p alloraO P n (d) non soddisfa la ProprietàN p. I casin≥3, d≥3, d<p<3d−2 sono ancora aperti (eccetton=d=3). Qui consideriamo uno di tali casi, precisamente proviamo cheO P n (3) soddisfa la ProprietàN 4 ∀n. Inoltre proviamo cheO P n (d) soddisfaN p ∀n≥p se e solo seO P p (d) satisfiesN p.相似文献
16.
Claudio Asci 《Journal of Theoretical Probability》2009,22(3):791-809
We consider the rate of convergence of the Markov chain X
n+1=A
X
n
+B
n
(mod p), where A is an integer matrix with nonzero eigenvalues, and {B
n
}
n
is a sequence of independent and identically distributed integer vectors, with support not parallel to a proper subspace
of Q
k
invariant under A. If
for all eigenvalues λ
i
of A, then n=O((ln p)2) steps are sufficient and n=O(ln p) steps are necessary to have X
n
sampling from a nearly uniform distribution. Conversely, if A has the eigenvalues λ
i
that are roots of positive integer numbers, |λ
1|=1 and |λ
i
|>1 for all
, then O(p
2) steps are necessary and sufficient.
相似文献
17.
V. G. Krotov 《Mathematical Notes》1997,62(4):439-448
In the critical case αp=n functions from the Hardy-Sobolev spacesH
α
p
(B
n
) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved
in the paper that the maximal operator associated with these regions is bounded as an operator fromH
α
p
(B
n
) toL
p
(ϖB
n
).
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 527–539, October, 1997.
Translated by N. K. Kulman 相似文献
18.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
19.
Let T
n
be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1
n
as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T
n
as follows A(n;T)=|{S
T
n
: 1
n
∈S, S≅T}|, and B(n;T)=|{S
T
n
:1
n
∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim
n→∞[A(n;T)/B(n;T)]=2ℓ;−1−1, for any tree T with ℓ leaves.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
Sharp estimates of the point-evaluation functional in weighted Bergman spaces L
p
a
(Ω, dν
α) and for the point-evaluation derivalive functional in Besov spaces B
p
(Ω) are obtained for bounded symmetric domains Ω in ℂ
n
.
Received October 25, 1999, Accepted December 6, 2000 相似文献