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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.
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
4.
Bruno de Malafosse 《Acta Mathematica Hungarica》2004,104(3):241-263
We deal with the sum and the product of particular BK spaces and give necessary and sufficient conditions to have w
α(λ) + w
β(μ) = w
α
+β
(μ). Some results on matrix transformations mapping the space w
α(λ) + w
β(μ) into a given BK space are also given. This study generalizes some results obtained in [7] and [8].
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
An elementary proof of the (known) fact that each element of the Banach spaceℓ
w
p
(X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ
w
p
(X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications
to spaces of compact operators on Banach sequence spaces are considered. 相似文献
6.
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
7.
K. L. Avetisyan 《Potential Analysis》2008,29(1):49-63
We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α
1,...,α
n
) with non-positive α
j
≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.
相似文献
8.
S. S. Volosivets 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(2):149-156
For Hausdorff operator with generating function having support in the unit ball of p-adic field ℚ
p
we give sufficient and necessary conditions of its boundedness in BMO-type spaces: BLO(ℚ
p
n
), Q
r
α,q
(ℚ
p
n
) and BMO
r
α,q
(ℚ
p
n
). Some embedding relations between these spaces and Besov spaces are established. 相似文献
9.
V. Kokilashvili 《Journal of Mathematical Sciences》2010,170(1):20-33
Boundedness criteria for the Calderón singular integral, Riesz transform and Cauchy singular integral in generalized weighted
grand Lebesgue spaces L
p),θ
w
, 1 < p < ∞, are studied. It is shown that an operator K of this type is bounded in L
p),θ
w
if and only if the weight w satisfies the Muckenhoupt A
p
condition. Bibliography: 15 titles. 相似文献
10.
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
11.
Veli B. SHAKHMUROV 《数学年刊B辑(英文版)》2008,29(1):95-112
This study focuses on the anisotropic Besov-Lions type spaces B^lp,θ(Ω;E0,E) associated with Banach spaces E0 and E. Under certain conditions, depending on l =(l1,l2,…,ln)and α=(α1,α2,…,αn),the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators D^α are bounded and compact, from B^l+s p,θ(Ω;E0,E) to B^s p,θ(Ω;Eα).These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties. 相似文献
12.
The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces
L
p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential
operators on the spaces
Lp(·)(\mathbbR +,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting
on L
p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential
operators on
\mathbbR+{\mathbb{R}_{+}} and local invertibility of singular integral operators on
\mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L
p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities. 相似文献
13.
Sharp estimates of the point-evaluation functional in weighted Bergman spaces L
p
a
(Ω, dν
α) and for the point-evaluation derivalive functional in Besov spaces B
p
(Ω) are obtained for bounded symmetric domains Ω in ℂ
n
.
Received October 25, 1999, Accepted December 6, 2000 相似文献
14.
The Besov spacesB
p
α,μ
(Γ) and Triebel-Lizorkin spacesF
p
α,μ
(Γ) with high order α∈R on a Lipschitz curve Γ are defined. when 1≤p≤∞, 1≤q≤∞. To compare to the classical case a difference
characterization of such spaces in the case |α|<1 is given also.
The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China. 相似文献
15.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
(i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
(ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
(iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
(iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
(v) | We investigate the properties of the operators from X α,p spaces to their predual. |
16.
Commutators of singular integrals on spaces of homogeneous type 总被引:1,自引:0,他引:1
In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular
integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables,
Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L
p
(w) when w belongs to the Muckenhoupt’s class A
p
, p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality
on spaces of homogeneous type, which we have not found previously in the literature. 相似文献
17.
Let Λ = (λ
k
) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference
sequence spaces associated with multiplier sequences i.e. w
0[A,Δ
m
,Λ,p], w
1[A,Λ
m
,Λ,p], w
∞[A,Δ
m
,Λ,p] and study their different properties. We also introduce Δ
Λ
m
-statistically convergent sequences and give some inclusion relations between w
1[Δ
m
,λ,p] convergence and Δ
Λ
m
-statistical convergence.
Communicated by Pavel Kostyrko 相似文献
18.
The central Campanato spaces and its application 总被引:2,自引:0,他引:2
Yang Dachun 《分析论及其应用》1994,10(4):85-99
Let 1<p<∞, α≥0 andK be a local field. In this paper, the author introduces the spaces J
p
α
(K) and the central Campanato spaces
as well as the Sp,α- and S
p,α
+
-type singular integrals. Then, the author investigates the behavior of these singular integrals and their altered operators
on these spaces.
The research was supported by the NNSF of China. 相似文献
19.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
20.
K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex
Song Li 《数学学报(英文版)》1999,15(3):395-406
An inverse theorem for the best weighted polynomial approximation of a function in
(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial
approximation in
, wherew
α is a Jacobi-type weight onS, 0<p ≤ ∞,S is a simplex andW
λ is a Freud weight. For Ditzian-TotikK-functionals onL
p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression. 相似文献