共查询到20条相似文献,搜索用时 31 毫秒
1.
Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w
p
Σα(X), w
p
Q
α(X) and wD
α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued
weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the
operators f*, S
(p)(f) and σ(p)(f) are obtained.
This research was supported by the National Science Foundation of China (No. 10371093). 相似文献
2.
In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space w
p
H
α
S
(X) is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy
regular martingale space w
p
H
α
S
(X). 相似文献
3.
Erdal Ekici 《Periodica Mathematica Hungarica》2007,54(1):77-84
The purpose of this paper is to introduce properties of the notion of α-compactness for fuzzy topological spaces. Moreover, α
c-compact spaces are introduced and properties of them are also discussed for fuzzy topological spaces.
相似文献
4.
Weak atomic decompositions of B-valued martingales with two-parameters in weak Hardy spaces w
p
Σα and w
p
H
α are established and the boundedness of sublinear operators on these spaces are proved. By using them, some characterizations
of the smoothness of Banach spaces are obtained. 相似文献
5.
JianYingNIE Xing Guo Nie GUO Wei LOU 《数学学报(英文版)》2005,21(6):1465-1474
Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type (L1,L1), and the corresponding maximal operators of the two-dimensional case are of weak type (Hi, L1). In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1. 相似文献
6.
Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces 总被引:2,自引:1,他引:1
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established. 相似文献
7.
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
8.
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
9.
In this paper, the boundedness of an oscillating multiplier m γ,β for different β on the Herz type spaces is obtained. This operator was initially studied by Wainger and Fefferman-Stein. Our results extend one of the main results in a paper by Xiaochun Li and Shanzhen Lu for the non-weighted case, if β is close to 1 or α is suitably large. For β ≥ 1, the results with no weights on the Herz type spaces are also new. 相似文献
10.
Boundedness of Multilinear Operators in Herz-type Hardy Space 总被引:1,自引:0,他引:1
Let κ∈ℕ. We prove that the multilinear operators of finite sums of products of singular integrals on ℝn are bounded from HK
α1,p1
q1
(ℝn) ×···×HK
αk,pk
qk
(ℝn) into HK
α,p
q
(ℝn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments
satisfied by the multilinear operators are also necessary when αj≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals
of any orders.
Received September 6, 1999, Revised November 17, 1999, Accepted December 9, 1999 相似文献
11.
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
12.
Veil B. SHAKHMUROV 《数学学报(英文版)》2006,22(5):1493-1508
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters. 相似文献
13.
An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying M
Δ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy
martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale
spaces.
This work was supported by the National Natural Science Foundation of China (Grant No. 10671147) 相似文献
14.
LetT
Ω,α
(0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theL
r
-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution
operators
. The smoothness conditions imposed on
are weaker than the corresponding known results. 相似文献
15.
Ushangi Goginava 《数学学报(英文版)》2011,27(10):1949-1958
The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ H
p
such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space L
p
. 相似文献
16.
Let 0<p≤1<q<0, andw
1
,w
2
∈ A
1
(Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the
homogeneous weighted Herz-type Hardy spacesH Kα, p
q(w1; w2) to the homogeneous weighted Herz spacesK
α, p
q
(w1; w2), provided α=n(1−1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spacesH K
α, p
q
(w
1;w
2) is also investigated.
Supported by the National Natural Science Foundation of China 相似文献
17.
In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces
and
, where ω1,ω3 ∈ A1-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study
the boundedness of some potential operators on these spaces.
Supported by the NNSF of China 相似文献
18.
Bruno De Malafosse Eberhard Malkowsky 《Rendiconti del Circolo Matematico di Palermo》2002,51(2):277-294
We give here some properties of the sets
α(uΔ) generalizing the space of generalized difference sequencesl
∞(uΔ). Then we study spaces related to the sets of sequences that are strongly convergent or strongly bounded. Next we define
from the sets of spaces that are (N,q) summable or bounded the sets of spaces that are (N,q)α-bounded orr-bounded. Then we give some properties of these spaces using Banach space of the forms
α. 相似文献
19.
M. M. Zarichnyi 《Mathematical Notes》1996,60(6):638-641
LetC be one of the absolute Borel classesM
α
,A
α
, with 1≤α<ω
1 or one of the absolute projective classesP
k
,k≥1. A map of ann-dimensional spaceX ∈ C onto the Hilbert cube which is ann-soft map in Shchepin's sense and universal in the class of maps of spaces of dimension smaller that or equal ton from the classC into separable metrizable spaces is constructed.
Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 845–850, December, 1996. 相似文献
20.
Dorothee Schueth 《Commentarii Mathematici Helvetici》1995,70(1):434-454
It is known that ifH
m is the classical (2m+1)-dimensional Heisenberg group, Γ a cocompact discrete subgroup ofH
m andg a left invariant metric, then (Γ/H
m, g) is infinitesimally spectrally rigid within the family of left invariant metrics. The purpose of this paper is to show that
for everym≥2 and for a certain choice of Γ andg, there is a deformation (Γ/H
m, g
α) withg=g
1 such that for every α≠1, (Γ/H
m, g
α)does admit a nontrivial isospectral deformation. For α≠1 the metricsg
α will not beH
m-left invariant, and the (Γ/H
m, gxα) will not be nilmanifolds, but still solvmanifolds. 相似文献