Uniform Approximation Properties for Spaces of Analytic Functions

We prove that the Banach space of bounded analytic functions and the disc algebra have the uniform bounded approximation property of order p for 1 < p < ∞.     

Para-Accretive Functions and Hardy Spaces

In this paper, we study the structure of the Hardy space H^p_b{H^p_b} associated with a para-accretive function b, which was introduced in Han et al. (J. Geom. Anal. 14:291–318, 2004). The main result is to establish a new atomic decomposition of H^p_b{H^p_b} . As applications, we obtain criterions for the boundedness of operators on H^p_b{H^p_b} and a characterization of the dual space of H^p_b{H^p_b} . The classification of H^p_b{H^p_b} and Calderón–Zygmund decomposition are also discussed.     

Real Functions in Weighted Hardy Spaces

We study the following problem: to describe weights w on the unit circle such that the analytic and antianalytic subspaces of the corresponding weighted space ^Lp(w) have nonzero intersection. In the special case p=2, the problem is equivalent to the well-known problem on exposed points in H ¹. We show that the property in question is local, i.e., it depends on local behavior of the weight w at each point of the unit circle. Some necessary and sufficient conditions in terms of the Herglotz integrals are obtained. Bibliography: 6 titles.     

Spectra of Analytic Toeplitz Tuples on Hardy Spaces

Let A be a complex algebra (with unit e), X a left A moduleand a = (a₁, ..., a_m) a commuting tuple of elements in A. FollowingTaylor [8], we have to consider the Koszul complex K_•(a,X) in order to define the joint spectrum of the tuple a. 1991Mathematics Subject Classification 47A13.     

Rational Approximation of Functions in Hardy Spaces

Subsequent to our recent work on Fourier spectrum characterization of Hardy spaces \(H^p({\mathbb {R}})\) for the index range \(1\le p\le \infty ,\) in this paper we prove further results on rational Approximation, integral representation and Fourier spectrum characterization of functions for the Hardy spaces \(H^p({\mathbb {R}}), 0 < p\le \infty ,\) with particular interest in the index range \( 0< p \le 1.\) We show that the set of rational functions in \( H^p({\mathbb {C}}_{+1}) \) with the single pole \(-i\) is dense in \( H^p({\mathbb {C}}_{+1}) \) for \(0<p<\infty .\) Secondly, for \(0<p<1\), through rational function approximation we show that any function f in \(L^p({\mathbb {R}})\) can be decomposed into a sum \(g+h\), where g and h are, in the \(L^p({\mathbb {R}})\) convergence sense, the non-tangential boundary limits of functions in, respectively, \( H^p({\mathbb {C}}_{+1})\) and \(H^{p}({\mathbb {C}}_{-1}),\) where \(H^p({\mathbb {C}}_k)\ (k=\pm 1) \) are the Hardy spaces in the half plane \( {\mathbb {C}}_k=\{z=x+iy: ky>0\}\). We give Laplace integral representation formulas for functions in the Hardy spaces \(H^p,\) \(0<p\le 2.\) Besides one in the integral representation formula we give an alternative version of Fourier spectrum characterization for functions in the boundary Hardy spaces \(H^p\) for \(0<p\le 1\).     

Dual Spaces of Weighted Spaces of Analytic Functions

Siberian Mathematical Journal -     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

解析函数在本性奇点的一些研究

用正规族理论,研究解析函数在本性奇点附近性质,得到解析函数及其导数在孤立本性奇点附近的一些结果.     

Removable Singularities for Anisotropic Elliptic Equations

We study a class of quasi-linear elliptic equations with model representative \(\sum _{i=1}^{n}(|u_{x_{i}}|^{p_{i}-2}u_{x_{i}})_{x_{i}}=0\) , which solutions have singularities on a smooth manifold. We establish the condition for removability of singularity on a manifold for solutions of such equations.     

Hyperplane Singularities of Analytic Functions of Several Complex Variables

A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.     

Lipschitz-Type Spaces and Hardy Spaces on Some Classes of Complex-Valued Functions

In this paper, we investigate the properties on some classes of complex-valued functions which satisfy certain elliptic equations. First, we discuss the Lipschitz-type spaces and Hardy spaces on these functions, and then we show that for a class of complex-valued functions, if it admits some bounded Dirichlet-type energy integral, then it has a harmonic majorant in the unit disk.     

Analytic Representation of CR Functions on Hypersurfaces with Singularities

We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.     

Criteria of the Removable Sets for the Weighted Spaces of Harmonic Functions

Sharp functional, capacity, and metric characteristics of removable sets for harmonic functions without fluxions in the weighted space L ¹ _p, with the Muckenhoupt weight are found. Bibliography: 3 titles.     

Hardy Spaces of Harmonic Functions on Homogeneous Isotropic Trees

A variational method for operator equations of the form Pu + δβ(u) ? f has been given in Dinca [1]. Here P is a (generally) nonlinear operator in a Hilbert space, β: H → ? ∞ is a convex, proper (β ≠ + ∞) and lower-semicontinuous functional and δβ(u) stands for the subdifferential of β at the point u. The present paper has two parts. The first part contents the main results of Dinca [1] without proofs. The second part discusses particular cases and applications to mechanics among which “the climatisation problem for non-linear elliptic equations” and its applications.     

Uniqueness Properties of Hardy Space Functions

We study the boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.     

On Hardy - Littlewood Maximal Functions in Orlicz Spaces

Let Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lim_s→ ∞ b(s) = + ∞. Then the following statements for the Hardy - Littlewood maximal function M f (x) are equivalent:

• 1 (i) there exist positive constants c₁ and s₀ such that
• 1 (ii) there exist positive constant c₂ and c₃ such that

.     

某类解析函数的性质

引入了解析函数类H的子类H(λ,α,A,B),通过利用Briot-Bouquet微分从属的方法,研究了它的从属关系、包含关系、属于H(λ,α,A,B),或属于其子类的充要条件.     

Order Structures in Banach Spaces of Analytic Functions

In this paper we consider some Banach spaces of analytic functions on the unit disk generated by the cone of analytic functions with monotone decreasing Taylor coefficients. We get that some of these spaces are Banach lattices with respect to this cone. Different ordered spaces of linear bounded operators acting between the previous spaces are also investigated, with emphasis on the so-called regular multipliers and Hankel operators.