The inclusions between the Besov spaces $B^q$, Bloch space $\mathcal{B}$ and standard weighted Bergman $A^p_\alpha$ are completely understood, but norms of corresponding inclusion operators in general unknown. In this work, we compute or estimate asymptotically these inclusions.

Let φ(z) = (φ 1 (z),. .. , φ n (z)) be a holomorphic self-map of U n and ψ(z) a holomorphic function on U n , where U n is the unit polydisk of C n. Let p ≥ 0, q ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operator W ψ,φ induced by ψ and φ to be bounded and compact between p-Bloch space B p (U n) and q-Bloch space B q (U n).

The aim of the present paper is to completely characterize boundedness and compactness a sum operator defined by some more complex products composition, multiplication, mth iterated radial derivative operators from Bloch-type spaces weighted-type on unit ball. In applications, all ball are also characterized.

Nosotros consideramos auto aplicaciones φ1, φ2 del disco unitario abierto bien como aplicaciones anaĺıticas ψ1, ψ2. Estas aplicaciones inducen diferencias de composición de operadores con peso actuando entre espacios de Banach pesados de funciones holomorfas y espacios de tipo Bloch con peso. En este art́ıculo damos condiciones necesarias y suficientes para que tal diferencia sea acotada, respec...

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...

We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object our concerns weighted mixed norm Bergman domains type II. These include: sampling, atomic decomposition, duality, boundary values, boundedness the projectors. Our analysis include Hardy spaces, and suitable generalizations classical Bloch Dirichlet spaces. One novelties in this work...