This paper studies a generalized class of linear operators acting on spaces of analytic functions, defined by Pnψ,φ(f)(z)=∑j=0nψj(z)f(j)(φ(z)), where ψ={ψ0,ψ1,…,ψn}⊂H(D) and φ∈S(D). This formulation encompasses several classical operators, including composition, weighted composition, differentiation–composition, and the Stević–Sharma operator. We focus on the action of Pnψ,φ from BMOA and analytic Besov spaces Bp into the Bloch space B, and provide necessary and sufficient conditions for boundedness and compactness. These results unify and extend many previously known characterizations and demonstrate the flexibility of the Pnψ,φ framework in the context of analytic operator theory.

This paper investigates the boundedness of multiplication operators Mψ between natural μ-Bloch-type spaces Bμ,nat(BX) (or their little μ-Bloch counterparts) and natural ω-Bloch-type spaces Bω,nat(BX) on the unit ball BX of a complex Banach space X. We establish complete characterizations for the boundedness of Mψ under varying conditions on the weight functions μ and ω, including specific cases such as logarithmic and power-weighted Bloch spaces. The results extend classical operator theory to infinite-dimensional settings, unifying prior work on finite-dimensional domains.

Shift invariant subspaces of large index in the Bloch space

In this paper, we introduce a weighted tent space and define associated weights. We show that some of these weights satisfy the Littlewood–Paley condition and others meet specific integral estimates. We study the closure of the weighted tent space in the Bloch space. Furthermore, we characterize the boundedness and compactness of the Volterra integration operator on weighted tent space. The paper ends with some open questions about the weights.

Mixed product differences of composition operators and Volterra operators on Bloch spaces

Composition Operators with Products of Analytic Symbols on Bloch Spaces

Pointwise lower bounds on the open unit disc $\mathbb{D} $ for the sum of the moduli of two analytic functions $f$ and $g$ (or their derivatives) are known in several cases, like $f,g$ belonging to the Bloch space $\mathcal{B} $, BMOA or the weighted Hardy space $H_\omega ^\infty $. We modify the proofs of two important cases, proved by Ramey-Ullrich and Abakumov-Doubtsov, for functions with little $o$ growth conditions.

In this paper, we integrate two foundational operators: a weighted composition operator, denoted by Wφ,ψ and two differentiation operators to construct a sandwich weighted composition operator, referred to as SWφ,ψ. We conduct a comprehensive analysis of the norms and essential norms of this operator within the framework of weighted Bloch spaces.

Bicomplex Bloch and little Bloch Spaces

Two-Weight Fractional Derivative on Bloch and Bergman Spaces

Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers

We propose in this work a practical approach to address the longstanding and challenging problem of quantum separability, leveraging the correlation matrices of generic observables. General separability conditions are obtained by dint of constructing the measurement-induced Bloch space, which in essence come from the intrinsic constraints in the space of quantum state. The novel approach can not only reproduce various established entanglement criteria, it may as well brings about some new results, possessing obvious advantages for certain bound entangled states and the high dimensional Werner states. Moreover, it is found that criteria obtained in our approach can be directly transformed into entanglement witness operators.

Abstract We prove the existence of functions in the Bloch space of the unit ball of with the property that, given any measurable function on the unit sphere , there exists a sequence , , converging to 1, such that for every , The set of such functions is residual in the little Bloch space. A similar result is obtained for the Bloch space of the polydisc.

ABSTRACTLet be a positive Borel measure on and . For , the generalized Hilbert operator is defined as follows: where, for denotes the th moment of the measure , and . In this paper, we characterize the measures for which is a bounded operator acting from Bergman space into . We determine the Hilbert–Schmidt class on for all . In addition, we also study the boundedness (resp. compactness) of acting from to the Bloch space.

Integral Characterizations of Hyperbolic Harmonic Bloch and Besov Spaces in the Real Unit Ball

Bounded and unbounded Bergman type projections on the Bloch space

On an inverse problem of approximation theory in the Bloch space

Weighted composition operators on Bicomplex bloch space

In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space X of holomorphic functions on the open unit polydisk into weighted‐type Banach spaces of holomorphic functions on . Under some restrictions on the space, we provide an approximation of the essential norm of such operators. We apply our results to the cases when X is the Hardy Hilbert space, the weighted Bergman Hilbert space, a weighted‐type Dirichlet space, and the Bloch space of the polydisk.

Abstract Let µ be a finite positive Borelmeasure on $[0,1)$ and $\alpha \gt -1$. The generalized integral operator of Hilbert type $\mathcal {I}_{\mu_{\alpha+1}}$ is defined on the spaces $H(\mathbb{D})$ of analytic functions in the unit disc $\mathbb{D}$ as follows: \begin{equation*}\mathcal {I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1} \frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t),\ \ f\in H(\mathbb{D}),\ \ z\in \mathbb{D} .\end{equation*}In this paper, we give a unified characterization of the measures µ for which the operator $\mathcal {I}_{\mu_{\alpha+1}}$ is bounded from the Bloch space to a Bergman space for all $\alpha \gt -1$. Additionally, we also investigate the action of $\mathcal {I}_{\mu_{\alpha+1}}$ from the Bloch space to the Hardy spaces and the Besov spaces.