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1.
This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema. We study general properties of such operators and their behavior on Lorentz gamma spaces. A particular emphasis is placed on elementary and comprehensive proofs. 相似文献
2.
3.
We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings and the identity . We also show that these spaces arise through real interpolation between and . Furthermore, we answer in a negative way the question posed in 12 whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability. 相似文献
4.
Shinya Moritoh Miyuki Niwa Takuya Sobukawa 《Proceedings of the American Mathematical Society》2006,134(8):2329-2334
In 1997 Ferreyra proved that it is impossible to extend the Stein-Weiss theorem in the context of Lorentz spaces. In this paper we obtain an interpolation theorem on Lorentz spaces over weighted measure spaces.
5.
Interpolation theorems on weighted Lorentz martingale spaces 总被引:2,自引:0,他引:2
Yong JIAO~ Li-ping FAN Pei-de LIU School of Mathematics Statistics Wuhan University Wuhan China 《中国科学A辑(英文版)》2007,50(9):1217-1226
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator. 相似文献
6.
Anna Kamińska Anca M. Parrish 《Journal of Mathematical Analysis and Applications》2008,343(1):337-351
We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kamińska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373]. 相似文献
7.
Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces. 相似文献
8.
A Banach lattice E is called p-disjointly homogeneous , 1≤p≤∞, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of ?p. Employing methods from interpolation theory, we clarify which r.i. spaces on [0,1] are p -disjointly homogeneous. In particular, for every 1<p<∞ and any increasing concave function φ on [0,1], which is not equivalent to neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function φ . Moreover, it is shown that given 1<p<∞ and an increasing concave function φ with non-trivial dilation indices, there is a unique p-disjointly homogeneous space among all interpolation spaces between the Lorentz and Marcinkiewicz spaces associated with φ. 相似文献
9.
In this paper, we obtain the(W H1ω, W L1ω) type estimate for the Marcinkiewicz integral and the(W H1 b,ω, W L1ω) type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition. 相似文献
10.
关于Marcinkiewicz积分高阶交换子在弱Hardy空间中的有界性 总被引:3,自引:0,他引:3
设μΩ带非光滑核Ω的Marcinkiewicz积分算子,m是正整数,肛μΩ,b^m是算子μΩ与BMO函数b产生的m阶交换子.利用原子分解和Littlewood—Paley技术,该文建立了高阶交换子μΩ,b^m在一类原子型弱Hardy空间WHb,m^p(0〈p≤1)中的有界性. 相似文献
11.
Joan Cerdà 《Journal of Mathematical Analysis and Applications》2005,304(1):269-295
We associate to every function space, and to every entropy function E, a scale of spaces Λp,q(E) similar to the classical Lorentz spaces Lp,q. Necessary and sufficient conditions for they to be normed spaces are proved, their role in real interpolation theory is analyzed, and a number of applications to functional and interpolation properties of several variants of Lorentz spaces and entropy spaces are given. 相似文献
12.
In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen [2]. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities. 相似文献
13.
In this paper, the authors consider the behaviors of a class of parametric Marcinkiewicz integrals μ
Ω
ρ
, μ
Ω,λ
*,ρ
and μ
Ω,S
ρ
on BMO(ℝ
n
) and Campanato spaces with complex parameter ρ and the kernel Ω in Llog+
L(S
n−1). Here μ
Ω,λ
*,ρ
and μ
Ω,S
ρ
are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley g
λ
*-function and the Lusin area function S, respectively. Under certain weak regularity condition on Ω, the authors prove that if f belongs to BMO(ℝ
n
) or to a certain Campanato space, then [μ
Ω,λ
*,ρ
(f)]2, [μ
Ω,S
ρ
(f)]2 and [μ
Ω
ρ
(f)]2 are either infinite everywhere or finite almost everywhere, and in the latter case, some kind of boundedness are also established. 相似文献
14.
DING Yong LU Shanzhen & ZHANG PuDepartment of Mathematics Beijing Normal University Beijing China Department of Information Computing Science Zhejiang Institute of Science Technology Hangzhou China 《中国科学A辑(英文版)》2004,47(1):83-95
In this paper the authors give the weighted weak L logL type estimates for a class of the higher order commutator generated by the Marcinkiewicz integral and a BMO function. In addition, the weak type norm inequalities for the Marcinkiewicz integral and its commutators with different weight functions are also discussed. 相似文献
15.
In this note, we obtain sharp L~p estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L~1(S~(n-1)). 相似文献
16.
In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given. 相似文献
17.
Xiaomei Wu 《分析论及其应用》2008,24(2):139-148
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi>0,m∑I=1βi=β,0<β<1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献
18.
设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2([0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作. 相似文献
19.
The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b(x) ∈ CBMOq(Rn) on homogeneous Morrey-Herz spaces is established. 相似文献
20.
给出了Marcinkiewicz积分在Herz型Hardy空间上的有界性证明。即当n(1 - 1q) ≤α 相似文献