共查询到20条相似文献,搜索用时 46 毫秒
1.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献
2.
Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition |V(z) − V(ζ)| ≤ w|z − ζ|, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A
p
weight on ℂ; i.e., the inequality
$
\left( {\frac{1}
{{\left| B \right|}}\int\limits_B {\omega d\sigma } } \right)\left( {\frac{1}
{{\left| B \right|}}\int\limits_B {\omega ^{ - \frac{1}
{{p - 1}}} d\sigma } } \right)^{p - 1} \leqslant c_0
$
\left( {\frac{1}
{{\left| B \right|}}\int\limits_B {\omega d\sigma } } \right)\left( {\frac{1}
{{\left| B \right|}}\int\limits_B {\omega ^{ - \frac{1}
{{p - 1}}} d\sigma } } \right)^{p - 1} \leqslant c_0
相似文献
3.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
4.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
5.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
6.
I. E. Chyzhykov 《Ukrainian Mathematical Journal》2007,59(7):1088-1109
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A
σ
ρ
of functions g(z) analytic in the unit disk
= {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
7.
Letf∈A ρ (ρ>1), whereA ρ denotes the class of functions analytic in ¦z¦ <ρ but not in ¦z¦≤ρ. For any positive integerl, the quantity Δ l,n?1(f; z) (see (2.3)) has been studied extensively. Recently, V. Totik has obtained some quantitative estimates for \(\overline {\lim _{n \to \infty } } \max _{\left| z \right| = R} \left| {\Delta _{l,n - 1}^ - \left( {f;z} \right)} \right|^{1/n} \) . Here we investigate the order of pointwise convergence (or divergence) of Δ l,n?1(f; z), i.e., we study \(B_1 \left( {f;z} \right) = \overline {\lim _{n \to \infty } } \left| {\Delta _{l,n - 1} \left( {f;z} \right)} \right|^{1/n} \) . We also study some problems arising from the results of Totik. 相似文献
8.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献 9.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
10.
In studying local harmonic analysis on the sphere Sn, R.S. Strichartz introduced certain zonal functions ϕ2(d(x, y)) which satisfy the equation
, where Δz is the Laplace operator and δ−y the Dirac measure. The explicit expression of the constant a (λ) is given by R.S. Strichartz in the case that n is odd. Appyling
the Apéry identity, we show in this paper that
for n even, where wn-1 is the surface area of Sn-1,
.
The author's research was supported by a grant from NSFC. 相似文献
11.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
12.
Let Δn−1 denote the (n − 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of Δn−1 obtained by starting with the full 1-dimensional skeleton of Δn−1 and then adding each 2−simplex independently with probability p. Let
denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity
13.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
14.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
15.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献 16.
Li Xin Zhang 《数学学报(英文版)》2008,24(4):631-646
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
17.
M. Nowak 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):363-374
In 1986 S. Axler [3] proved that forf∈L
a
2
the Hankel operator
is compact if and only iff is in the little Bloch space {itB}{in0}. In this note we show that the same is true for
, 1<p<∞. Moreover we prove that
is ⋆-compact if and only if
as |z|→1−. 相似文献
18.
Rong HUANG Kun Yang WANG 《数学学报(英文版)》2007,23(7):1327-1332
A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as follows:
Theorem Suppose f ∈ L(En-1), n≥ 3. If f satisfies the condition
1/θ^n-1∫D(x,θ)|f(y)-f(x)|dy=O(1/|logθ|),as θ→0+,
at every point x in a set E of positive measure in Σn-1, then the Cesàro means of critical order ,n-2/2 of the Fourier-Laplace series of f converge to f at almost every point x in E. 相似文献
19.
The generalized Roper-Suffridge extension operator Ф(f) on the bounded complete Reinhardt domain Ω in Cn with n ≥ 2 is defined by Φrn,β2,γ2,…,βn,γn(f)(z)=(rf(z1/r),(rf(z1/r)/z1)β2(f'(z1/r))γ2z2,…,(rf(z1/r)/z1)βn(f'(z1/r)γnzn) for (z1,z2,…,zn) ∈Ω, where r = r(Ω) = sup{|z1| (z1,z2,…,zn) ∈ Ω},0 ≤ γj ≤ 1 -βj,0 ≤ βj ≤ 1,and we choose the branch of the power functions such that (f(z1)/z1)βj |z1=0 = 1 and (f′(z1))γj |z1=0 =1,j = 2,…,n. In this paper, we prove that the operator Фrn,β2,γ2,…,βn,γn(f) is from the subset of S*α(U) to S*α(Ω)(0 ≤ α < 1) on Ω and the operator Фrn,β2,γ2,…, βn,γn(f) preserves the starlikeness of order α or the spirallikeness of type β on Dp for some suitable constantsβj,γj,pj, where Dp ={(z1,z2,…,zn) ∈ Cn ∑nj=1|zj|pj < 1} (pj > 0, j = 1,2,…,n), U is the unit disc in the complex plane C, and Sα* (Ω) is the class of all normalized starlike mappings of order α on Ω. We also obtain that Φrn,β2,γ2,…,γn(f) ∈ S*α(Dp) if and only if f ∈ S*a(U) for 0 ≤ α < 1 and some suitable constants βj,γj,pj. 相似文献
20.
Let II be a bounded symmetric domain, ω ⇉ I a bounded subdomain, and let
denote the weighted Bergman space of holomorphic square integrable functions on I. Let Tλ, ω be the Berezin-Toeplitz operator on
with symbol χΩ and kth eigenvalue λ
k
(T
λ,Ω). We prove that for δ1 sufficiently close to 0 and δ2 sufficiently close to 1 the estimate
|