The main purpose of this paper is to develop some methods investigate the Schwarz type lemmas holomorphic mappings and pluriharmonic in Banach spaces. Initially, we extend classical spaces, then apply these extensions establish a sharp Bloch theorem for on homogeneous unit balls ℂn obtain boundary Furthermore, improve generalize planar harmonic into forms present applications Additionally, usin...

In this paper we study continuity, boundedness from below and compactness of composition operators between μ-Bloch spaces for very general weights μ.

Talagrand showed in [7] that in general the logn factor is necessary. However, the main result of Naor and Schechtman [5] is that a stronger version of the inequality, without the logarithmic factor, holds for UMD spaces, a subclass of Banach spaces that contains in particular all Lp spaces for 1< p <∞. Naor and Schechtman also prove a family of inequalities generalizing Pisier’s inequality. Pi...

Abstract The paper considers two notions of logarithmic dichotomy for discrete skew-evolution semiflows in Banach spaces. We establish the relation between them, we give a characterization uniform Zabczyk type and sufficient criteria dichotomy.