共查询到20条相似文献,搜索用时 31 毫秒
1.
Ferenc Weisz 《数学学报(英文版)》2010,26(9):1627-1640
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, e∞) to W(Lp,e∞). This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W(L1, e∞) velong to L1. 相似文献
2.
Simon [J. Approxim. Theory,
127, 39–60 (2004)] proved that the maximal operator σα,κ,* of the (C, α)-means of the Walsh–Kaczmarz–Fourier series is bounded from the martingale Hardy space H
p
to the space L
p
for p > 1 / (1 + α), 0 < α ≤ 1. Recently, Gát and Goginava have proved that this boundedness result does not hold if p ≤ 1 / (1 + α). However, in the endpoint case p = 1 / (1 + α ), the maximal operator σα,κ,* is bounded from the martingale Hardy space H
1/(1+α) to the space weak- L
1/(1+α). The main aim of this paper is to prove a stronger result, namely, that, for any 0 < p ≤ 1 / (1 + α), there exists a martingale f ∈ H
p
such that the maximal operator σα,κ,*
f does not belong to the space L
p
. 相似文献
3.
Summary Let (Ω,A) be a measurable space, let Θ be an open set inR
k
, and let {P
θ; θ∈Θ} be a family of probability measures defined onA. Let μ be a σ-finite measure onA, and assume thatP
θ≪μ for each θ∈Θ. Let us denote a specified version ofdP
θ
/d
μ
byf(ω; θ).
In many large sample problems in statistics, where a study of the log-likelihood is important, it has been convenient to impose
conditions onf(ω; θ) similar to those used by Cramér [2] to establish the consistency and asymptotic normality of maximum likelihood estimates.
These are of a purely analytical nature, involving two or three pointwise derivatives of lnf(ω; θ) with respect to θ. Assumptions of this nature do not have any clear probabilistic or statistical interpretation.
In [10], LeCam introduced the concept of differentially asymptotically normal (DAN) families of distributions. One of the
basic properties of such a family is the form of the asymptotic expansion, in the probability sense, of the log-likelihoods.
Roussas [14] and LeCam [11] give conditions under which certain Markov Processes, and sequences of independent identically
distributed random variables, respectively, form DAN families of distributions. In both of these papers one of the basic assumptions
is the differentiability in quadratic mean of a certain random function. This seems to be a more appealing type of assumption
because of its probabilistic nature.
In this paper, we shall prove a theorem involving differentiability in quadratic mean of random functions. This is done in
Section 2. Then, by confining attention to the special case when the random function is that considered by LeCam and Roussas,
we will be able to show that the standard conditions of Cramér type are actually stronger than the conditions of LeCam and
Roussas in that they imply the existence of the necessary quadratic mean derivative. The relevant discussion is found in Section
3.
This research was supported by the National Science Foundation, Grant GP-20036. 相似文献
4.
If f∈L2[0, 1] and g*∈L2[0, 1] is the best non-decreasing approximation to f, then it's shown that ‖f−g*‖2=‖f−θ(f)‖2, where θ(f) denotes the Hardy-Littlewood maximal function of f. 相似文献
5.
Ushangi Goginava 《Periodica Mathematica Hungarica》2009,59(2):173-183
The main aim of this paper is to prove that there exists a martingale f ∈ H
12/▭ such that the restricted maximal operators of Fejér means of twodimensional Walsh-Fourier series and conjugate Walsh-Fourier
series does not belong to the space weak-L
1/2. 相似文献
6.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献
7.
E. P. Golubeva 《Journal of Mathematical Sciences》2006,133(6):1611-1621
Let S2(q) be the set of primitive forms in the space S2(Γ0(q)) of holomorpic Γ0(q)-cusp forms of weight 2. Let f ∈ S2(q) and let Lf(S) be the L-function of f(z). It is proved that the set {log Lf(1), f ∈ S2(q)} has a limit distribution function. The rate of convergence to this limit function is estimated. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 15–32. 相似文献
8.
Ferenc Weisz 《Constructive Approximation》2011,34(3):421-452
A general summability method of more-dimensional Fourier transforms is given with the help of a continuous function θ. Under some weak conditions on θ we show that the maximal operator of the ℓ
1–θ-means of a tempered distribution is bounded from H
p
(ℝ
d
) to L
p
(ℝ
d
) for all d/(d+α)<p≤∞ and, consequently, is of weak type (1,1), where 0<α≤1 depends only on θ. As a consequence we obtain a generalization of the one-dimensional summability result due to Lebesgue, more exactly, the
ℓ
1–θ-means of a function f∈L
1(ℝ
d
) converge a.e. to f. Moreover, we prove that the ℓ
1–θ-means are uniformly bounded on the spaces H
p
(ℝ
d
), and so they converge in norm (d/(d+α)<p<∞). Similar results are shown for conjugate functions. Some special cases of the ℓ
1–θ-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations. 相似文献
9.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2000,6(4):389-401
The two-parameter dyadic martingale Hardy spacesH
p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series
is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H
1
#
, L1), where the Hardy space H
1
#
is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H
1
#
converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too. 相似文献
10.
We prove weighted strong inequalities for the multilinear potential operator Tf{\cal T}_{\phi} and its commutator, where the kernel ϕ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type
estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator Mj,LB\mathcal{M}_{\varphi,L^{B}} associated to an essentially nondecreasing function φ and to the Orlicz space L
B
for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator Tf{\cal T}_{\phi}. 相似文献
11.
N. V. Lazakovich S. P. Stashulenok O. L. Yablonskii 《Lithuanian Mathematical Journal》1999,39(2):196-202
In this paper, we consider problems of approximation of stochastic θ-integrals (θ)∫
0
t
f(B(s))dB(s) with respect to a Brownian motion by sums of the form ∑
k=1
p
fn(B
n
θ
(tk-1))[B
n
θ
(tk)-B
n
θ
(tk-1], where the sequences {fn,n∈∕#x007D; and {[B
n
θ
,n∈∕} are convolution-type approximations of the functionf and Brownian motionB.
Belorussian State University, F. Skoryna ave. 4, 220050 Minsk, Belorus. Translated from Lietuvos Matematikos Rinkinys, Vol.
39, No. 2, pp. 248–256, April–June, 1999.
Translated by V. Mackevičius 相似文献
12.
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier series. Equivalent conditions
are derived for the uniform and L
1-norm convergence of the θ-means σ
n
θ
f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case θ is an element
of Feichtinger’s Segal algebra
, then these convergence results hold. Some new sufficient conditions are given for θ to be in
. A long list of concrete special cases of the θ-summation is listed. The same results are also provided in the context of
Fourier transforms, indicating how proofs have to be changed in this case.
This research was supported by Lise Meitner fellowship No M733-N04 and the Hungarian Scientific Research Funds (OTKA) No T043769,
T047128, T047132. 相似文献
13.
Ferenc Weisz 《分析论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded
from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H
1
#
(T×T), L1(T2)), where the Hardy space H
1
#
(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H
1
#
(T×T)⊃LlogL(T
2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces
Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too.
This research was made while the author was visiting the Humboldt University in Berlin supported by the Alexander von Humboldt
Foundation. 相似文献
14.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
15.
F. Weisz 《Acta Mathematica Hungarica》2007,116(1-2):47-59
The duality between martingale Hardy and BMO spaces is generalized for Banach space valued martingales. It is proved that if X is a UMD Banach space and f ∈ L
p(X) for some 1 < p < ∞ then the Vilenkin-Fourier series of f converges to f almost everywhere in X norm, which is the extension of Carleson’s result.
This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship
No. M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No. T043769, T047128, T047132. 相似文献
16.
Pedro E. Ferreira 《Annals of the Institute of Statistical Mathematics》1982,34(1):423-431
Summary Let {p(x, θ): θ∈Θ} be a family of densities where θ=(θ1,θ2), being θ1 ∈ Θ1 ak-dimensional parameter of interest, θ2 ∈ Θ2 a nuisance parameter and Θ=Θ1×Θ2. To estimate θ1, vector estimating equations g(x,θ1)=(g1(x,θ1),...,gk(x,θ1))=0 are considered. The standardized form of g(x,θ1) is defined as gs=(Eθ(∂g/∂θ′1))−1g. Then, within the classG
1 of unbiased equations (i.e. satisfying Eθ(g)=0 (θ∈Θ)), an equationg
*=0 is said to be optimum if the covariance matrices ofg
s andg
s
*
are such that
is non-negative definite for allg∈
G
1 and θ∈Θ. Sufficient conditions for optimality are discussed and, in particular, conditions for the optimality of the maximum
conditional likelihood equation are analyzed. Special attention is given to non-regular cases. In addition, measures of the
information about θ1 contained in an estimating equation are presented and a Rao-Blackwell theorem is given.
CIENES 相似文献
17.
In this paper, a natural R
+
n+1
extension of singular integrals, i.e.,T
κ:f→K*φ
t
*t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C1 and u-Mw, w∈A∞, then Tk is of type (Lp(udx), Lp(dμ)). As a related topic, a maximal operator
is proved to be of type
, where
, provided (dμ, udx) ∈C1 and u∈ A∞.
Supported by National Science Foundation of China 相似文献
18.
V. V. Kapustin 《Journal of Mathematical Sciences》2007,141(5):1538-1542
Let θ be an inner function, let K
θ
= H
2 ⊖ θH
2, and let Sθ : Kθ → Sθ be defined by the formula Sθf = Pθzf, where f ∈ Kθ is the orthogonal projection of H2 onto Kθ. Consider the set A of all trace class operators L : Kθ → Kθ, L = ∑(·,un)vn, ∑∥un∥∥vn∥ < ∞ (un, vn ∈ Kθ), such that ∑ūn vn ∈ H
0
1
. It is shown that trace class commutators of the form XSθ − SθX (where X is a bounded linear operator on Kθ) are dense in A in the trace class norm. Bibliography: 2 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 54–61. 相似文献
19.
An Application of a Mountain Pass Theorem 总被引:3,自引:0,他引:3
We are concerned with the following Dirichlet problem:
−Δu(x) = f(x, u), x∈Ω, u∈H
1
0(Ω), (P)
where f(x, t) ∈C (×ℝ), f(x, t)/t is nondecreasing in t∈ℝ and tends to an L
∞-function q(x) uniformly in x∈Ω as t→ + ∞ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0,
0 > θF(x, s) ≤f(x, s)s, for all |s|≥M and x∈Ω, (AR)
is no longer true, where F(x, s) = ∫
s
0
f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming
(AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable
conditions on f(x, t) and q(x). Our methods also work for the case where f(x, t) is superlinear in t at infinity, i.e., q(x) ≡ +∞.
Received June 24, 1998, Accepted January 14, 2000. 相似文献
20.
Given a∈L
1(ℝ) and A the generator of an L
1-integrable family of bounded and linear operators defined on a Banach space X, we prove the existence of almost automorphic solution to the semilinear integral equation u(t)=∫
−∞
t
a(t−s)[Au(s)+f(s,u(s))]ds for each f:ℝ×X→X almost automorphic in t, uniformly in x∈X, and satisfying diverse Lipschitz type conditions. In the scalar case, we prove that a∈L
1(ℝ) positive, nonincreasing and log-convex is already sufficient. 相似文献