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1.
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
2.
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
3.
Imre Patyi 《Mathematische Annalen》2003,326(3):443-458
Let X be one of the Banach spaces c
0
, ℓ
p
, 1≤p<∞; Ω⊂X pseudoconvex open, a holomorphic Banach vector bundle with a Banach Lie group G
*
for structure group. We show that a suitable Runge-type approximation hypothesis on X, G
*
(which we also prove for G
*
a solvable Lie group) implies the vanishing of the sheaf cohomology groups H
q
(Ω, 𝒪
E
), q≥1, with coefficients in the sheaf of germs of holomorphic sections of E. Further, letting 𝒪Γ (𝒞Γ) be the sheaf of germs of holomorphic (continuous) sections of a Banach Lie group bundle Γ→Ω with Banach Lie groups G, G
*
for fiber group and structure group, we show that a suitable Runge-type approximation hypothesis on X, G, G
*
(which we prove again for G, G
*
solvable Lie groups) implies the injectivity (and for X=ℓ1 also the surjectivity) of the Grauert–Oka map H
1
(Ω, 𝒪Γ)→H
1
(Ω, 𝒞Γ) of multiplicative cohomology sets.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L20, 32L05, 46G20
RID="*"
ID="*" Kedves Laci Móhan kisfiamnak.
RID="*"
ID="*" To my dear little Son 相似文献
4.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
5.
Spaces of analytic functions of Hardy-Bloch type 总被引:1,自引:1,他引:0
For 0<p≤∞ and 0<q≤∞, the space of Hardy-Bloch type ℬ(p,q) consists of those functionsf which are analytic in the unit diskD such that (1−r)M
p
(r,f′)⊂L
q
(dr/(1−r)). We note that ℬ(∞,∞) coincides with the Bloch space ℬ and that ℬ⊂ℬ(p,∞) for allp. Also, the space ℬ(p,p) is the Dirichlet spaceD
p−1
p
.
We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about
the mean growth of the ℬ(p,q). In particular, we prove that iff is an analytic function inD and 2≤p<∞, then the conditionM
p
(r,f′)=O((1−r)−1), asr→1, implies that
. This result is an improvement of the well-known estimate of Clunie and MacGregor and Makarov about the integral means of
Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question
of characterizing the univalent functions in the spaces ℬ(p,2), 0<p<∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces
ℬ(p,2) andD
p−1
p
.
The first and third authors were supported by grants from “E1 Ministerio de Educación y Ciencia”, Spain (MTN2004-00078 and
MTN2004-21420-E) and by a grant from “La Junta de Andalucía” (FQM-210).
The second author was supported in part by MNZŽS Grant, No. ON144010, Serbia. 相似文献
6.
For 0<p<∞, let Hp(R
n) denote the Lebesgue space for p>1 and the Hardy space for p ≤1. In this paper, the authors study Hp(R
n)×Hq(R
n)→Hr(R
n) mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the
standard fractional integral with the Calderón-Zygmund operator. The authors prove that such mapping properties hold if and
only if these operators satisfy certain cancellation conditions.
Supported by the NNSF and the National Education Comittee of China. 相似文献
7.
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
8.
In this note we extend the results in [1] to high dimensions. Let f∈Hp (Tn), 0<p<1, n≥1 andσ
δ
, f denote the Riesz means of f at the critical index δ=n/p−(n+1)/2. We have the following estimate:
were 0<s≤2 and
, is the K-functional in Hp(Tn).
Supported by NSFC 相似文献
9.
YangChangsen 《高校应用数学学报(英文版)》2001,16(3):285-289
Abstract. Suppose H is a complex Hilbert space, AH (△) denotes the set of all analytic operator functions on 相似文献
10.
We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL
p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl
p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL
1 containsl
p, for somep in the interval [1, 2]. 相似文献
11.
Let {M
r,s
(p,p′)}1≤r≤p−1,1≤s≤p′−1 be the irreducible Virasoro modules in the (p,p′)-minimal series. In our previous paper, we have constructed a monomial basis of ⊕
r=1
p−1
M
r,s
(p,p′) in the case 1<p′/p<2. By ‘monomials’ we mean vectors of the form
, where φ
−n
(r′,r):M
r,s
(p,p′)→M
r′,s
(p,p′) are the Fourier components of the (2,1)-primary field and |r
0,s〉 is the highest weight vector of
. In this article, we introduce for all p<p′ with p≥3 and s=1 a subset of such monomials as a conjectural basis of ⊕
r=1
p−1
M
r,1(p,p′). We prove that the character of the combinatorial set labeling these monomials coincides with the character of the corresponding
Virasoro module. We also verify the conjecture in the case p=3.
相似文献
12.
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
13.
Shangquan BU 《数学年刊B辑(英文版)》2011,32(2):293-302
The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H
p
($
\mathbb{T}
$
\mathbb{T}
d
;X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property (α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of
sets of bounded linear operators. It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property (α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. 相似文献
14.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
15.
K. M. D'yakonov 《Journal of Mathematical Sciences》1996,78(2):131-141
Let ϕ be a unimodular function on the unit circle
and let Kp(ϕ) denote the kernel of the Toeplitz operator Tϕ in the Hardy space Hp, p≥1;
. Suppose Kp(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in
Kp(ϕ). One of the main results is as follows.
Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q−1=p−1+r−1. Suppose |ϕ|≡1 on
and ϕ∈W
r
1
(i.e.,
). Then Kp(ϕ)⊂W
q
1
. Moreover, for any f∈Kp(ϕ) we have ‖f′‖q≤c(p, r)‖ϕ′‖r ‖f‖. Bibliography: 19 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21.
Translated by K. M. D'yakonov. 相似文献
16.
A result previously known only for certain ordered Banach spaces is generalized to arbitrary real Banach spaces. Let ℒ be
the Banach algebra of operators generated by theL-projections of a real Banach spaceU, and let ℳ (U
* be the bounded operators on the dual spaceU
* with adjoint in ℒ(U
**. Then the adjoint operation maps ℒ (U) onto ℳ (U
*). In particular, anyM-projection ofU
* is weak* continuous.
Supported in part by the National Science Foundation. 相似文献
17.
Jan van Neerven 《Positivity》2007,11(3):461-467
We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces LXp, where X is a Banach space and 1≤ p<∞, and extend the result to vector-valued Banach function spaces EX, where E is a Banach function space with order continuous norm.
The author is supported by the ‘VIDI subsidie’ 639.032.201 in the ‘Vernieuwingsimpuls’ programme of the Netherlands Organization
for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281. 相似文献
18.
Assume thatf is an integer transcendental solution of the differential equationP
n
(z, f, f′)=P
n−1(z, f, f′, ... f
(p)), whereP
n
andP
n−1 are polynomials in all variables, the degree ofP
n
with respect tof andf′ is equal ton, and the degree ofP
n−1 with respect tof, f′, ... f
(p) is at mostn−1. We prove that the order ρ of growth off satisfies the relation 1/2≤ρ<∞. We also prove that if ρ=1/2, then, for a certain real ν, in the domain {z: ν<argz<ν+2π}/E
*, whereE
* is a certain set of disks with finite sum of radii, the estimate lnf(z)=z
1/2 (β+o(1)), β∈C, holds forz=re
iϕ,r≥r(ϕ)≥0. Furthermore, on the ray {z: argz=ν}, the following relation is true: ln‖f(re
iν)‖=o(r
1/2),r→+∞,r>0,
, where Δ is a certain set on the semiaxisr>0 with mes Δ<∞.
“L'vivs'ka Politekhnika” University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 69–77,
January, 1999. 相似文献
19.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
20.
Jarosaw Górnicki 《Rendiconti del Circolo Matematico di Palermo》1997,46(1):89-118
In this paper we study in Banach spaces the existence of fixed points of (nonlinear) asymptotically regular semigroups. We
establish for these semigroups some fixed point theorems in spaces with weak uniform normal structure, in a Hilbert space,
inL
p
spaces, in Hardy spacesH
p
and in Sobolev spacesW
r.p
for 1<p<∞ andr≥0, in spaces with Lifshitz’s constant greater than one. These results are the generalizations of [8, 10, 16]. 相似文献