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1.
We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules.
As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined
on L
ℱ
p
(ℰ, H) and generated by measure-preserving transformations on Ω, where H is a Hilbert space, L
p
(ℰ, H) (1 ⩽ p < ∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, ℰ, P), F a sub σ-algebra of ℰ, and L
ℱ
p
(ℰ(E,H) the complete random normed module generated by L
p
(ℰ, H). 相似文献
2.
William A. Veech 《Journal d'Analyse Mathématique》1990,55(1):117-171
The cotangent bundle ofJ (g, n) is a union of complex analytic subvarieties, V(π), the level sets of the function “singularity pattern” of quadratic differentials.
Each V(π) is endowed with a natural affine complex structure and volume element. The latter contracts to a real analytic volume
element, Μπ, on the unit hypersurface, V1(π), for the Teichmüller metric. Μπ is invariant under the pure mapping class group, γ(g, n), and a certain class of functions is proved to be Lp(Μπ), 0 <p < 1, over the moduli space V1(π)/γ (g, n). In particular, Μπ(V1(π)/γ(g, n)) < ∞, a statement which generalizes a theorem by H. Masur.
Research supported by NSF-MCS-8219148 and NSF-DMS-8521620. 相似文献
3.
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
4.
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
5.
Let 1<α≦β<∞ andF be an arbitrary closed subset of the interval [α,β]. An Orlicz sequence spacel
φ (resp. an Orlicz function spaceL
φ(μ)) with associated indices α and β is found in such a way that the set of valuesp for which thel
p-space is isomorphic to a complemented subspace ofl
φ (resp.L
φ(μ)) is precisely the given setF (resp.F ∪ {2}). Also, a recent result of Hernández and Peirats [1] is extended showing that, even for the case in which the indices
satisfy αφ
∞<2<βφ
∞, there exist minimal Orlicz function spacesL
φ(μ) with no complemented copy ofl
p for anyp ≠ 2.
Supported in part by CAICYT grant 0338-84. 相似文献
6.
A. Bonilla F. Pérez-González A. Stray R. Trujillo-González 《Journal d'Analyse Mathématique》1997,73(1):65-89
This paper is concerned with several approximation problems in the weighted Hardy spacesH
p(Ω) of analytic functions in the open unit disc D of the complex plane ℂ. We prove that ifX is a relatively closed subset of D, the class of uniform limits onX of functions inH
p(Ω) coincides, moduloH
p(Ω), with the space of uniformly continuous functions on a certain hull ofX which are holomorphic on its interior. We also solve the simultaneous approximation problems of describing Farrell and Mergelyan
sets forH
p(Ω), giving geometric characterizations for them. By replacing approximating polynomials by polynomial multipliers of outer
functions, our results lead to characterizations of the same sets with respect to cyclic vectors in the classical Hardy spacesH
p(D), 1 ⪯p < ∞.
Dedicated to Professor Nácere Hayek on the occasion of his 75th birthday. 相似文献
7.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1983,35(1):401-406
Summary A parameter which may be represented as a functionalT(F) of a distribution functionF may be estimated by the “statistical function”T(F
n
), whereF
n
is the empirical distribution function. Recently, Boos and Serfling (1979, Florida State University Statistics Report No.
M 499) obtained sufficient conditions for the Berry-Esseen theorem to hold forT(F
n
)-T(F) and applied the results to derive rates of convergence inL
∞ forL-estimates. The present note complements their work by obtaining theL
p
-rates of convergence, 1≦p<∞ forT(F
n
)-T(F) and its application toL-estimates. 相似文献
8.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
9.
Yong Ding Senhua Lan 《分析论及其应用》2006,22(4):339-352
Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 < p < 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 < p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn). 相似文献
10.
F. A. Shamoyan 《Journal of Mathematical Sciences》2006,139(2):6491-6495
Let ϕ(r) = (ϕ1(r1), …, ϕn(rn)) be a vector-valued function on R
+
n
. A necessary and sufficient condition is obtained under which any function f ∈, H∞ (D
n
), f(z) ≠ 0, z ∈, D
n
, is cyclic in the corresponding weighted space Lp(ϕ), where D
n
is the unit polydisk in C
n. Bibliography: 13 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 226–234. 相似文献
11.
Liguang Liu 《Frontiers of Mathematics in China》2007,2(4):599-611
Let ℐ(ℝn) be the Schwartz class on ℝn and ℐ∞(ℝn) be the collection of functions ϕ ∊ ℐ(ℝn) with additional property that
for all multiindices γ. Let (ℐ(ℝn))′ and (ℐ∞(ℝn))′ be their dual spaces, respectively. In this paper, it is proved that atomic Hardy spaces defined via (ℐ(ℝn))′ and (ℐ∞(ℝn))′ coincide with each other in some sense. As an application, we show that under the condition that the Littlewood-Paley
function of f belongs to L
p(ℝn) for some p ∊ (0,1], the condition f ∊ (ℐ∞(ℝn))′ is equivalent to that f ∊ (ℐ(ℝn))′ and f vanishes weakly at infinity. We further discuss some new classes of distributions defined via ℐ(ℝn) and ℐ∞(ℝn), also including their corresponding Hardy spaces.
相似文献
12.
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
13.
Loukas GRAFAKOS 《中国科学A辑(英文版)》2008,51(12):2253-2284
Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a dimension n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] a... 相似文献
14.
Martin Kružík 《Applications of Mathematics》2007,52(6):529-543
We study convergence properties of {υ(∇u
k
)}k∈ℕ if υ ∈ C(ℝ
m×m
), |υ(s)| ⩽ C(1+|s|
p
), 1 < p < + ∞, has a finite quasiconvex envelope, u
k
→ u weakly in W
1,p
(Ω; ℝ
m
) and for some g ∈ C(Ω) it holds that ∫Ω
g(x)υ(∇u
k
(x))dx → ∫Ω
g(x)Qυ(∇u(x))dx as k → ∞. In particular, we give necessary and sufficient conditions for L
1-weak convergence of {det ∇u
k
}
k∈ℕ to det ∇u if m = n = p.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday
This work was supported by the grants IAA 1075402 (GA AV ČR) and VZ6840770021 (MŠMT ČR). 相似文献
15.
Rainer Wittmann 《Israel Journal of Mathematics》1987,59(1):8-28
LetT be a positive linear contraction inL
p (1≦p<∞), then we show that lim ‖T
pf −T
n+1
f‖
p
≦(1 − ε)21/p
(f∈L
p
+
, ε>0 independent off) implies already limn
n→∞ ‖T
nf −T
n+1
n+1f ‖p
p=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown. 相似文献
16.
We give necessary conditions and sufficient conditions for sequences of reproducing kernels (kΘ(·, λn))n ≥ 1 to be overcomplete in a given model space KΘp where Θ is an inner function in H∞, p ∈ (1, ∞), and where (λn)n ≥ 1 is an infinite sequence of pairwise distinct points of
Under certain conditions on Θ we obtain an exact characterization of overcompleteness. As a consequence we are able to describe
the overcomplete exponential systems in L2 (0, a). 相似文献
17.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
18.
Andreas Fr?hlich 《Annali dell'Universita di Ferrara》2000,46(1):11-19
We consider weights of Muckenhoupt classA
q, 1<q<∞. For a bounded Lipschitz domain Ω⊂ℝn we prove a compact embedding and a Poincaré inequality in weighted Sobolev spaces. These technical tools allow us to solve
the weak Neumann problem for the Laplace equation in weighted spaces on ℝn, ℝn
+, on bounded and on exterior domains Ω with boundary of classC
1, which will yield the Helmholtz decomposition ofL
ω
q(Ω)n for general ω∈A
q. This is done by transferring the method of Simader and Sohr [4] to the weighted case. Our result generalizes a result of
Farwig and Sohr [2] where the Helmholtz decomposition ofL
ω
p(Ω)n is proved for an exterior domain and weights of Muckenhoupt class without singularities or degeneracies in a neighbourhood
of ϖΩ.
Sunto In questo lavoro consideriamo dei pesi della classe di MuckenhouptA q, 1<q<∞. Per un dominio limitato lipschitziano Ω⊂ℝn, dimostriamo una immersione compatta ed una disuguaglianza di Poincaré in spazi di Sobolev con peso. Questa tecnica ci consente di risolvere il problema debole di Neumann per l’equazione di Laplace in spazi pesati in ℝn, ℝn + in domini limitati ed in domini esterni con frontiera di classeC 1, che conduce alla decomposizione di Helmholtz diL ω q(Ω)n per un qualsiasi ω∈A q. Il risultato è ottenuto trasferendo il metodo di Simader e Sohr [4] al caso pesato. Quello qui presente estende un risultato di Farwig e Sohr [2] dove la decomposizione di Helmholtz diL ω q(Ω)n è dimostrata per domini esterni e pesi della classe di Muckenhoupt privi di singolarità in un intorno di ϖΩ.相似文献
19.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):135-140
Summary LetF be a distribution function over the real line. DefineR
p(y)=∫|x−y|pdF(x) forp≧1. Forp>1 there is a unique minimizer ofR
p(·), sayγ
p. Under mild conditions onF it is shown that
exists and that the limit is a median. Thus, one could use this limit as a definition of a unique median. Also it is shown
that
whereR is the right extremity ofF andL is the left extremity ofF provided that −∞<L≦R<∞. A similar result is available ifL=−∞,R=∞, yetF has symmetric tails. 相似文献
20.
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