从$\alpha$-Bloch空间到$Q_K$型空间的复合算子

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ： Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK（p,q） and QK,0（p,q） spaces are discussed, where 0 〈 α 〈 ∞.     

Approximative compactness and continuity of metric projector in Banach spaces and applications

First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~ ,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.     

Weighted composition operators from F（p,q, s） spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.     

Isometric immersions into warped product spaces

This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.     

A note on the generalized Marcinkiewicz integral operators with rough kernels

In this paper,we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn×Rm.Under the condition that Ω is a function in certain block spaces,which is optimal in some senses,the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.     

Local Lipschitz-α Mappings and Applications to Sublinear Expectations

The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.     

Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces

Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.     

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.     

Spectrum of L-fuzzy Prime Ideals of a Distributive Lattice

A topological space denoted by Fspec(D),called L-fuzzy prime spectrum of a bounded distributive lattice D is introduced.This space Fspec(D) is compact and it contains a subspace homeomorphic with the prime spectrum of D which is dense in it.The correspondence associating D to the topological space Fspec(D) is shown to define a contravarient functor from the category of bounded distributive lattices into the category of compact topological spaces.     

COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

Let D be the unit disc and H(D) be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H(D) : f(z) =sum from k=o to ∞ ak(z + 1)k, z∈ D, ‖f‖2 = sum from k=o to ∞ |ak|24k < ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.     

Linear-Fractional Composition Operators in Several Variables

We investigate properties of linear-fractional composition operators C_φ on Hardy and Bergman spaces of the ball in that are motivated by a formula for the self-commutator [C_φ^* ,C_φ]. In particular, we characterize when certain commutators [C_φ, C_σ] are compact, and give conditions under which is compact, where is multiplication by the monomial z^β. Our results allow us to determine when C_φ is essentially normal, for φ belonging to a large class of linear-fractional symbols.     

Herz Classes and Toeplitz Operators in the Disk

In this paper we decompose into diadic annuli and consider the class S_p,q of Toeplitz operators T_φ for which the sequence of Schatten norms belongs to ℓ^q, where φ_n = φχ A_n. We study the boundedness and compactness of the operators in S_p,q and we describe the operators T_φ , φ ≥ 0 in these spaces in terms of weighted Herz norms of the averaging operator of the symbols φ.     

Spectral Exponent of Finite Sums of Weighted Positive Operators in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-Spaces

In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form

General Hardy’s inequalities for functions nonzero on the boundary

Consider Hardy’s inequalities with general weight ϕ for functions nonzero on the boundary. By an integral identity in C ¹( ), define Hilbert spaces H _k ¹ (Ω, ϕ) called Sobolev-Hardy spaces with weight ϕ. As a corollary of this identity, Hardy’s inequalities with weight ϕ in C ¹ ( ) follow. At last, by Hardy’s inequalities with weight ϕ = 1, discuss the eigenvalue problem of the Laplace-Hardy operator with critical parameter (N − 2)²/4 in H ¹ ₁ (Ω).      

A Class of Operators on Weighted Bergman Spaces

This paper studies the connection between an analytic function φ on the unit disk and a certain type of operators induced by φ on weighted Bergman spaces A ^α of analytic functions on . The general theme is the interplay between smoothness conditions on φ and the S _p -norms of the operators induced by φ.      

Kernels of Toeplitz operators,smooth functions,and Bernstein type inequalities

Let ϕ be a unimodular function on the unit circle and let K_p(ϕ) denote the kernel of the Toeplitz operator T_ϕ in the Hardy space H^p, p≥1; . Suppose K_p(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in K_p(ϕ). One of the main results is as follows. Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q⁻¹=p⁻¹+r⁻¹. Suppose |ϕ|≡1 on and ϕ∈W _r ¹ (i.e., ). Then K_p(ϕ)⊂W _q ¹ . Moreover, for any f∈K_p(ϕ) we have ‖f′‖_q≤c(p, r)‖ϕ′‖_r ‖f‖. Bibliography: 19 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21. Translated by K. M. D'yakonov.     

Extension to R + n+1 of singular integrals and fractional integrals

In this paper, a natural R ₊ ⁿ⁺¹ extension of singular integrals, i.e.,T _κ:f→K*φ _t *t with K a standard C-Z kernel and ϕ usual one, is investigated. One of the main results is: Let (dμ, udx) ∈C₁ and u-Mw, w∈A_∞, then T_k is of type (L^p(udx), L^p(dμ)). As a related topic, a maximal operator is proved to be of type , where , provided (dμ, udx) ∈C₁ and u∈ A_∞. Supported by National Science Foundation of China     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence:

Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution

Let D be any division ring with an involution,Hn （D） be the space of all n × n hermitian matrices over D. Two hermitian matrices A and B are said to be adjacent if rank（A - B） = 1. It is proved that if φ is a bijective map from Hn（D）（n ≥ 2） to itself such that φ preserves the adjacency, then φ^-1 also preserves the adjacency. Moreover, if Hn（D） ≠J3（F2）, then φ preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices.     

Hilbert-Schmidt Hankel Operators on the Bergman Space of Planar Domains

In this paper we study the problem of the membership of H _ϕ in the Hilbert-Schmidt class, when and Ω is a planar domain. We find a necessary and sufficient condition.We apply this result to the problem of joint membership of H _φ and in the Hilbert-Schmidt class. Using the notion of Berezin Transform and a result of K. Zhu we are able to give a necessary and sufficient condition. Finally, we recover a result of Arazy, Fisher and Peetre on the case with φ holomorphic.