Compact composition operators between weighted Bergman spaces on convex domains in ℂ n

It is shown that a compact composition operator on a weighted Bergman space over a smoothly bounded strongly convex domain in ⁿ can have no angular derivative. Also, sufficient conditions for the boundedness and the compactness of composition operators defined on Hardy and weighted Bergman spaces are obtained, for situations in which each of the target spaces is enlarged in a natural way.     

Eversive maps of bounded convex domains in ℂ n+1

A duality principle, relating the geometry of the Kobayashi metric with the CR geometry of the boundaries of smoothly bounded, strongly convex domains in ℂ ⁿ⁺¹ is established. A characterization of the holomorphic Jacobi vector fields of those domains is also given.     

Toeplitz and Hankel matrices on ℂ n

It is known that the characterizations of the Toeplitz operatorT onH ² and also the Hankel operatorH onH ² by using the simple unilateral shiftT _z . Recently, some characterization of the normal Toeplitz matrix truncated on ⁿ is given by D.R.Farenick, M. Krupnik, N. Krupnik and W. Y. Lee [1] and, independently, by T.Ito [2]. In this paper, we shall give some characterizations of the Toeplitz matrix and also the Hankel matrix truncated on ⁿ .Dedicated to Professor Masanori Fukamiya on his 88th birthday     

A direct theorem for strictly convex domains in ℂn

For a strictly covex C²-smooth domain Ω??ⁿ and a function f ? Λ^α(Ω) holomorphic in Ω, we construct polynomials p_N, deg p_N<-N, such that $$\left| {f(z) - p_N (z)} \right| \leqslant CN^{ - \alpha } ,z \in \bar \Omega .$$ Bibliography: 12 titles.     

q-subharmonicity and q-convex domains in ℂ n

In this paper we study q-subharmonic and q-plurisubharmonic functions in ? ⁿ . Next as an application, we give the notion of q-convex domains in ? ⁿ which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.     

The Gleason''''s problem on mixed norm spaces in convex domains

Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.     

The boundedness of multilinear Calderón–Zygmund operators on Hardy spaces

In this paper, we study the boundedness of the multilinear Calderón–Zygmund operators on products of Hardy spaces.     

Pluriharmonic mappings and linearly connected domains in ℂ n

In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball \(\mathbb{B}^n \) of ? ⁿ . The results are generalizations of conditions of Chuaqui and Hernández that relate the univalence of planar harmonic mappings with linearly connected domains, and show how such domains can play a role in questions regarding injectivity in higher dimensions. In addition, we extend recent work of Hernández and Martín on a shear type construction for planar harmonic mappings, by adapting the concept of stable univalence to pluriharmonic mappings of the unit ball \(\mathbb{B}^n \) into ? ⁿ .     

Convolution operators in A ?∞ for convex domains

We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ ⁿ and have a polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of all domains is given in terms of low bounds of the Laplace transformation of analytic functionals defining the operators.     

Bounded projections and duality on spaces of holomorphic functions in the unit ball ofℂ n

In this paper three Banach spacesA ₀(),A andA ¹() of functions holomorphic in the unit ballB of ⁿ are defined. We exhibit bounded projections fromC ₀(B) ontoA ₀(), fromL ¹(B) ontoA ¹(), and fromL(B) ontoA(). Using these projections, we show thatA ₀()* A ¹() andA ¹()* A().Supported in part by the National Natural Science Foundation of China.     

Boundedness of Calderón-Zygmund operators in product Hardy spaces

By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.     

Cesàro-type operators on Hardy, BMOA and bloch spaces

Let H ^p, p ∈ (0, ∞], BMOA and B ^a, a ∈ (0, ∞) be the classical p-Hardy, analytic BMO(∂) (bounded mean oscillation on the unit circle) and a-Bloch space on the unit disk. In this paper, we prove that the Cesàro-type operator: C ^α, α ∈ (−1, ∞) is bounded on H ^p, p ∈ (0, ∞) and on B ^a, a ∈ (1, ∞), but, unbounded on H ^∞, BMOA and B ^a, a ∈ (0, 1]. In particular, we give an answer to the Stempak’s open problem.     

Multilinear Calderón Zygmund operators on variable exponent Morrey spaces over domains

The boundedness of multilinear singular integrals of Calderón-Zygmund type on product of variable exponent Lebesgue spaces over both bounded and unbounded domains are obtained. Further more, the boundedness for this type multilinear operators on product of variable exponent Morrey spaces over domains is shown in the paper.     

Hausdorff operators on p-adic linear spaces and their properties in Hardy, BMO, and Hölder spaces

Sufficient conditions for the boundedness of p-adic matrix operators in Hardy, Hölder and BMO spaces are obtained. These conditions are expressed in terms of the determinant of the matrix and its norm in a p-adic linear space.     

Spectral properties of generalized Cesàro operators on Hardy and weighted Bergman spaces

We investigate spectral properties of integral operators of the form

Density of the polynomials in Hardy and Bergman spaces of slit domains

It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\} and with the property that the analytic polynomials are dense in the Bergman space \mathbbA^t(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma) . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in H^t(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma) ; improving upon a result in an earlier paper.