Bloch Space Research Articles

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.

Differences of Composition Operators on Bloch Type Spaces

In 2007, T. Hosokawa and S. Ohno gave the sufficient and necessary conditions of the boundedness and compactness of differences of composition operators on the Bloch space. On this base, this paper will generalize these conditions of the boundedness and compactness of differences of composition operators on the Bloch type space. AMS subject classifications: 52B10, 65D18, 68U05, 68U07

Some characterizations of harmonic Bloch and Besov spaces

The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω-α-Bloch space and characterize it in terms of $$\omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{x - y}}} \right|$$ and $$\omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{\left| x \right|y - x'}}} \right|$$ where ω is a majorant. Similar results are extended to harmonic little ω-α-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G.Ren, U.Kahler (2005).

Essential norm of generalized weighted composition operators from the Bloch space to the Zygmund space

In this paper, we give some estimates of the essential norm for generalized weighted composition operators from the Bloch space to the Zygmund space. Moreover, we give a new characterization for the boundedness and compactness of the operator.

Carleson measures, riemann-stieltjes operators and multipliers on F(p, q, s) spaces in the unit ball of ℂn

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F(p, q, s) spaces in the unit ball of ℂn, which contain many classical function spaces, such as the Bloch space, BMOA and Qs spaces. The boundedness and compactness of these operators on F(p,q,s) spaces are characterized by means of an embedding theorem, i.e., F(p,q,s) spaces boundedly embedded into the tent-type spaces T∞p,s (μ).

Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

The spectra of invertible weighted composition operators $uC_\varphi$ on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when $\varphi$ is a parabolic or elliptic automorphism of the unit disc. In the case of a hyperbolic automorphism $\varphi$, exact expressions for the spectral radii of invertible weighted composition operators acting on the Bloch and Dirichlet spaces are derived.

The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation

LetBbe the real unit ball inRnandf∈CN(B). Given a multi-indexm=(m1,…,mn)of nonnegative integers with|m|=N, we set the quantitysupx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ, x≠y,where0≤γ≤1andα+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.

Logarithmic Bloch space and its predual

We consider the space B1log?, of analytic functions on the unit disk D, defined by the requirement ?D|f?(z)|?(|z|) dA(z) < ?, where ?(r) = log?(1/(1?r)) and show that it is a predual of the ?log?-Bloch? space and the dual of the corresponding little Bloch space. We prove that a function f(z)=??n=0 an zn with an ? 0 is in B1 log? iff ??n=0 log?(n+2)/(n+1) < ? and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in B1 log?. Some properties of the Cesaro and the Libera operator are considered as well.

On the compactness of the Stević-Sharma operator on the logarithmic Bloch spaces

On the compactness of the Stević-Sharma operator on the logarithmic Bloch spaces

Boundedness from below of composition operators on α-logarithmic Bloch spaces

Boundedness from below of composition operators on α-logarithmic Bloch spaces

Generalized weighted composition operators from H∞ to the logarithmic Bloch space

In this paper, we give three different characterizations for the boundedness and compactness of generalized weighted composition operators from the space of bounded analytic function to the logarithmic Bloch space.

Products of Composition and Differentiation Operators from Bloch intoQKSpaces

The boundedness and compactness of the product of differentiation and composition operators from Bloch spaces intoQKspaces are discussed in this paper.

Logarithmic Bloch spaces and their weighted composition operators

The objective of this paper is to characterize the continuity and to estimate the essential norm of the weighted composition operators acting from the logarithmic Bloch spaces to any Bloch-type spaces.

On characterizations of Bloch spaces and Besov spaces of pluriharmonic mappings

We characterize the Bloch spaces and Besov spaces of pluriharmonic mappings on the unit ball of ${\mathbb{C}}^{n}$ by using the following quantity: $\sup_{\rho(z,w)< r,z\neq w}\frac{(1-|z|^{2})^{\alpha}(1-|w|^{2})^{\beta}|\hat{D}^{(m)}f(z)-\hat {D}^{(m)}f(w)|}{|z-w|}$ , where $\alpha+\beta=n+1$ , $\hat{D}^{(m)}=\frac{\partial ^{m}}{\partial z^{m}}+\frac{\partial^{m}}{\partial\bar{z}^{m}}$ , $|m|=n$ . This generalizes the main results of (Yoneda in Proc. Edinb. Math. Soc. 45:229-239, 2002) in the higher dimensional case.

On an integral-type operator from the Bloch space to mixed norm spaces

Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0)=0, where H(B) is the space of all holomorphic functions on the unit ball B of Cn. In this paper we investigate the following integral-type operatorDφgf(z)=∫01Df(φ(tz))g(tz)dtt,f∈H(B),where Df is the fractional derivative of f ∈ H(B). The boundedness and compactness of the operators Dφg between mixed norm spaces and Bloch spaces in the unit ball are studied.

Boundedness and compactness of the composition operators from &amp;lt;italic&amp;gt;u&amp;lt;/italic&amp;gt;-Bloch space to &amp;lt;italic&amp;gt;v&amp;lt;/italic&amp;gt;-Bloch space on the first Hua domains

In this paper, we introduce a weighted Bloch space and discuss the boundedness and compactness of composition operators Cφ from the u -Bloch space βu (HE I ) to the v -Bloch space βv (HE I ), and obtain the necessary condition and sufficient condition on the boundedness and compactness of composition operators Cφ on the first Hua domains.

Characterizations of Weighted Bloch Space by Q p, ω-Type Spaces of Quaternion-Valued Functions

Characterizations of Weighted Bloch Space by <i>Q _{p, ω}</i>-Type Spaces of Quaternion-Valued Functions

Differences of integral-type operators from weighted Bergman spaces to Bloch spaces of the unit ball

We investigate the following integral-type operatorwhere with and the collection of all the holomorphic self-mappings of The boundedness and compactness of the differences of integral-type operators acting from the weighted Bergman space to the Bloch space (or the little Bloch space) in the unit ball were characterized. At the same time, we obtained the estimates for the essential norms of the differences.

Composition Operators from p-Bloch Space to q-Bloch Space on the Fourth Cartan-Hartogs Domains

We obtain new generalized Hua’s inequality corresponding to YIV(N,n;K), where YIV(N,n;K) denotes the fourth Cartan-Hartogs domain in CN+n. Furthermore, we introduce the weighted Bloch spaces on YIV(N,n;K) and apply our inequality to study the boundedness and compactness of composition operator Cϕ from βp(YIV(N,n;K)) to βq(YIV(N,n;K)) for p≥0 and q≥0.

Some new characterizations of Bloch type spaces of infinite matrices via Schur multipliers

We consider the innite matrix version B(D, l2) of the Bloch space. In this paperwe complement the results in the recent book [18] by deriving some new characteriza-tions of B(D, l2) and related spa ...