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1.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
2.
We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ : θ∈θ} representing an important sublinear expectation- G-expectation E[·]. We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions Lip(Ω) in order to prove that Cb(Ω) belongs to the completion of Lip(Ω) under the natural norm E[|·|]. 相似文献
3.
Let G be a locally compact group. For 1 < p < ∞, it is well-known that f * g exists and belongs to Lp(G) for all f, g
Lp
(G) if and only if G is compact. Here, for 2 < p < ∞, we show that f * g exists for all f, g
Lp(G) if and only if G is compact. We also show that this result does not remain true for 1 < p ≤ 2.
Received: 23 April 2006 相似文献
4.
We classify graph C
*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to
strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C
*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence
of such algebras, without using the boundary operator algebra. A direct relation is given between the K
1-group of the algebra and the cycle space of the graph.
We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K
0(
Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University
College. 相似文献
5.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
6.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
7.
In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
(φp(u'))'+β/r φp(u')-γ |u'|^p/u + g(r)=0,0〈r〈1,
subject to the Dirichlet boundary conditions: u(0) = u(1) =0, where φp(s) = |sl^P-2s,p 〉 2,β 〉0, γ〉(p-1)/p (β + 1), and g(r) ∈ C^1 [0, 1] with g(r) 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution. 相似文献
(φp(u'))'+β/r φp(u')-γ |u'|^p/u + g(r)=0,0〈r〈1,
subject to the Dirichlet boundary conditions: u(0) = u(1) =0, where φp(s) = |sl^P-2s,p 〉 2,β 〉0, γ〉(p-1)/p (β + 1), and g(r) ∈ C^1 [0, 1] with g(r) 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution. 相似文献
8.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
9.
In this paper, we get W
1,p
(R
n
)-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and
Tananka’s results.
Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural
Science Foundation of China. 相似文献
10.
Let E be a Galois extension of ℚ of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of cannot be factored nontrivially into a product of L-functions over E.
Next, we compare the n-level correlation of normalized nontrivial zeros of L(s, π1)…L(s, π
k
), where π
j
, j = 1,…, k, are automorphic cuspidal representations of , with that of L(s,π). We prove a necessary condition for L(s, π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific , j = 1,…,k. In particular, if π is not invariant under the action of any nontrivial σ ∈ Gal
E/ℚ, then L(s, π) must equal a single L-function attached to a cuspidal representation of and π has an automorphic induction, provided L(s, π) can factored into a product of L-functions over ℚ. As E is not assumed to be solvable over ℚ, our results are beyond the scope of the current theory of base change and automorphic
induction.
Our results are unconditional when m,m
1,…,m
k
are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.
The first author was supported by the National Basic Research Program of China, the National Natural Science Foundation of
China (Grant No. 10531060), and Ministry of Education of China (Grant No. 305009). The second author was supported by the
National Security Agency (Grant No. H98230-06-1-0075). The United States Government is authorized to reproduce and distribute
reprints notwithstanding any copyright notation herein 相似文献
11.
M. G. Grigoryan 《Russian Mathematics (Iz VUZ)》2008,52(5):20-31
For any 0 < ? < 1 one can find a measurable set E ? [0, 1] with the measure |E| > 1 ? ? such that for each function f(x) ε L 1 (0, 1) a function g(x) ε L 1 (0, 1) exists such that it coincides with f (x) on E, its Fourier—Walsh series converges to it in the metric of L 1 (0, 1), and all nonzero terms of the sequence of Fourier coefficients of the new function obtained by the Walsh system have the modulo decreasing order; consequently, the greedy algorithm for this function converges to it in the L 1 (0, 1)-norm. 相似文献
12.
Roberta Tognari 《Potential Analysis》2007,26(2):163-188
We consider the operator in L
2(B, ν) and in L
1(B, ν) with Neumann boundary condition, where U is an unbounded function belonging to for some q ∈(1, ∞), B is the possibly unbounded convex open set in where U is finite and ν(dx) = C exp (−2U (x))dx is a probability measure, infinitesimally invariant for N
0. We prove that the closure of N
0 is a m-dissipative operator both in L
2(B, ν) and in L
1(B, ν). Moreover we study the properties of ergodicity and strong mixing of the measure ν in the L
2 case.
相似文献
13.
In this article we study the problem of extending Fourier
Multipliers on L
p
(T) to those on L
p
(R)
by taking convolution with a kernel, called a summability
kernel. We characterize the space of such kernels
for the cases p = 1 and p = 2. For other values of p we give a
necessary condition for a function to be a
summability kernel. For the case p = 1, we present
properties of measures which are transferred from M(T) to
M(R) by summability kernels. Furthermore it is
shown that every l
p
sequence can be extended to some
L
q
(R) multipliers for certain values of p and q. 相似文献
14.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
15.
16.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
17.
Zhang Pu Wu Huoxiong 《高校应用数学学报(英文版)》2005,20(4):455-461
Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO(R^n). It is proved that μΩ,bis bounded from the Hardy space H^1 (R^n) into the weak L^1(R^n) space. 相似文献
18.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data,
f
D
, has one derivative in L
p
(D) of the boundary and the Neumann data, f
N
, is in L
p
(N). We find a p
0 > 1 so that for p in an interval (1, p
0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L
p
.
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation. 相似文献
19.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
20.
Christian Wegner 《manuscripta mathematica》2009,128(4):469-481
Let X be a finite aspherical CW-complex whose fundamental group π
1(X) possesses a subnormal series with a non-trivial elementary amenable group G
0. We investigate the L
2-invariants of the universal covering of such a CW-complex X. The main result is the proof of the vanishing of the L
2-torsion under the condition that π
1(X) has semi-integral determinant. We further show that the Novikov–Shubin invariants are positive. 相似文献