Composition Operators on α-Bloch Spaces of the Unit Ball

The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball.     

Hardy-Orlicz Spaces and Their Multiplication Operators

In this paper some formulae on the relationship between Hardy and Hardy Orlicz spaces are presented, and multiplication operators on Hardy-Orlicz spaces are discussed.     

Boundedness of the θ-type Calderon-Zygmund Operators on Weighted Herz-type

In this paper, we will discuss the boundedness of θ-type Calderdn-Zygmund operator on weighted Herz-type Hardy spaces.     

A Remark on the Boundedness of Calderón-Zygmund Operators in Non-homogeneous Spaces

Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.     

The Boundedness of Composition Operators on Triebel–Lizorkin and Besov Spaces with Different Homogeneities

In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.     

Weighted Composition Operators of H∞ into α-Bloch Spaces on the Unit Ball

In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in C^n.     

Weighted Composition Operators from α-Bloch Spaces to H^∞

The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted composition operator.     

Boundedness of Multilinear Operators on Herz Type Spaces： Extreme Cases

In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases.     

Nested Commutators of Calderon-Zygmund Operators on Product Spaces

Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L~P boundedness of the nested commutators is proved on product spaces, where 1＜p＜∞.     

Boundedness of Multilinear Caldern–Zygmund Singular Operators on Morrey–Herz Spaces with Variable Exponents

In this paper,we introduce Morrey–Herz spaces M K˙(·)q,p(·)(Rn) with variable exponents α(·) and p(·),and prove the boundedness of multilinear Caldern–Zygmund singular operators on the product of these spaces.     

The Boundedness of the Commutator for Riesz Potential Associated with Schr dinger Operator on Morrey Spaces

Let L =-△ + V be the Schr dinger operator on Rd, where △ is the Laplacian on Rdand V≠0 is a nonnegative function satisfying the reverse H lder's inequality.The authors prove that Riesz potential Iβand its commutator [b, Iβ] associated with L map from Mp,qα,vinto Mp1,q1α,v.     

Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

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.     

Additive Maps Preserving Similarity of Operators on Banach Spaces

Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.     

Boundeness of a Class of Maximal Operators on H~p Spaces on Compact Lie Groups

In this paper we discuss the weak type(H^p,L^p) boundedness of a class of maximal operators T*^ψ and themaximal strong mean boundedness of a family of the operators ｛T^ψ｝ on the atomic H^p spaces on compact Lic groups.Also,we obtain the correspoding convergent results.     

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.     

Boundedness of Multilinear Singular Integral Operators on Homogeneous Groups

Let G be a homogeneous group.In this paper,the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G.As its special case,the corresponding result of multilinear Calderón-Zygmund operators can be obtained.     

Bilinear Operators on Herz-type Hardy Spaces on Locally Compact Vilenkin Groups

Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.     

Boundedness of the Maximal Operator on Lipα（R^n）（0〈α〈1）

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｌｏｃａｌｌｙｉｎｔｅｇｒａｂｌｅｆｕｎｃｔｉｏｎｆ（ｘ）ｂｅｌｏｎｇｓｔｏＬｉｐα（Ｒｎ）,ｉｆｔｈｅｒｅｉｓａｃｏｎｓｔａｎｔＣ,ｓｕｃｈｔｈａｔｆｏｒｅｖｅｒｙｘ,ｙ∈Ｒｎ｜ｆ（ｘ）－ｆ（ｙ）｜≤Ｃ｜ｘ－ｙ｜α　　ＴｈｅｓｍａｌｌｅｓｔｃｏｎｓｔａｎｔＣｓａｔｉｓｆｉｅｓａｂｏｖｅｉｓｃａｌｌｅｄＬｉｐｓｃｈｉｔｚｎｏｒｍｏｆｆａｎｄｉｓｄｅｎｏｔｅｄｂｙｙｆｙ∧α．Ｂｙ［１］,ｆ∈Ｌｉｐα（Ｒｎ）ｅｑｕｉｖａｌｅｎｔｔｏｆ∈εα,２,ｗｈｅｒｅεα,２＝…     

Continuity for Maximal Multilinear Bochner-Riesz Operators on Hardy and Herz Hardy Spaces

Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.     

Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces

Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure.