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1.
Let[b,T]be the commutator generated by a Lipschitz function b ∈ Lip(β)(0<β<1)and multiplierT.The authors studied the boundedness of[b,T]on the Lebesgue spaces and Hardy spaces.  相似文献   

2.
张学军  ZHAO Qian 《数学进展》2004,33(1):125-127
Let B be the unit ball in C^n. By H(B) we denote the class of all holomorphic functions on B and H^∞ denotes the class of all bounded holomorphic functions on B.  相似文献   

3.
Let (→b)=(b1,…,bm),bi∈Λβi(Rn),1≤i≤m,0<βi<β,0<β<1,[(→b),T]f(x)=∫Rn,(b1(x)-b1(y))…(bm(x)-bm(y)))K(x-y)f(y)dy where K is a Calder(o)n-Zygmund kernel.In this paper,we show that[(→b),T] is bounded from Lp (Rn) to Fβ,∞p(Rn),as well as[(→b,Iα)] from Lp(Rn) to Fβ,∞p(Rn),where 1/q=1/p-α/n.  相似文献   

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We give a decomposition of the Hardy space Hz^1(Ω) into "div-curl" quantities for Lipschitz domains in R^n. We also prove a decomposition of Hz^1(Ω) into Jacobians det Du, u ∈ W0^1,2 (Ω,R^2) for Ω in R^2. This partially answers a well-known open problem.  相似文献   

7.
Let L^p(Ω, H^n) indicate the L^P-space of the maps for Heisenberg group target. In this paper some new properties are obtained for the space L^p(Ω, H^n)  相似文献   

8.
Jian Yong  WANG 《数学学报(英文版)》2009,25(10):1729-1740
For 0 〈β 〈 1, the author once wrote a paper to deal with the representation problem of the conjugate cone [L^β[0, 1]β^* of complex β-nanach space L^β[0, 1]. In this paper, replacing [0, 1] with a Borel finite measure space (Ω,M,μ) and replacing the complex field C with a Banach space X, we study the representation problem of the conjugate cone [L^β(μ, X)]β^* of L^β(μ, X), and obtain [L^β(μ, X)]β^*≌L^∞ M^+(μ, S), called the Quasi-Representation Theorem of [L^β(μ, X)]β^*.  相似文献   

9.
In [4], a new family W(L^p(x), Lm^q) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p(x) (R) and the global component is a weighted Lebesgue space Lm^q (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W (L^p(x), Lm^q) = L^q (R). Later we give some characterization of Wiener amalgam space W (L^p(x), Lm^q).In Section 3 we define the Wiener amalgam space W (FL^p(x), Lm^q) and investigate some properties of this space, where FL^p(x) is the image of L^p(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.  相似文献   

10.
In this paper,the authors establish the weighted (L^p,L^q) estimates for a class of multilinear oscillatory singular integrals with smooth phases.Certain endpoint estimates are also considered.  相似文献   

11.
We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces R+^n+1. The characterization of the boundedness and compactness of the generalized area operator from LP(]Rn) to Lq(IRn) is investigated in terms of s-Carleson measures with 1 〈 p, q 〈 +∞. In the case of p = q = 1, the weak type estimate is also obtained.  相似文献   

12.
本文讨论了与H ̄(p,α)空间有关的乘子问题,得到为H ̄(p,α)到H ̄(q,α)或H ̄(p,α)到l ̄q乘子的充分条件.作为应用,证明了一个关于H ̄(p,α)函数的Taylor系数的猜想.  相似文献   

13.
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles  相似文献   

14.
LetUbeastandarduniverseandUbeanenlargednonstandarduniversewithrespecttoU.XisatopologicalspacewhichincludedintheindividualsetofU,thatis,XX.Definition1 Foreachx∈X,wedefinem(x)=∩{V:V∈Ix}andcallm(x)themonadofx(Ixistheopenneighborhoodofx).Wewritey≈xfo…  相似文献   

15.
给出了L^p(E)(1〈p〈∞)的自反性的一个构造性证明.  相似文献   

16.
Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type (2, 2), i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type (2, 2). The main result is that the order is 1, 2, 3, 4 or infinite.  相似文献   

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In this paper,by use of the Schauder fixed-point theorem,the existence of solution of (k,n-k) Conjugate boundary value problems in Banach spaces is investigated.  相似文献   

19.
This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometric mapping from the unit sphere S(t(2)^∞) to S(L^1(μ) can be (real) linearly isometrically extended.  相似文献   

20.
In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T(D(VN,F)),which acting on the normal Siegel domain D(VN,F)is simple and transitive,and prove that the maximal connected automorphism group of T(D(VN,F))is its maximal connected inner automorphism group.  相似文献   

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