By using the concept of the weak subordination, we examine the stability a class of analytic functions in the unit disk is said to be stable if it is closed under weak subordination for a class of admissible functions in complex Banach spaces. The stability of analytic functions in the following classes is discussed: Bloch class, little Bloch class, hyperbolic little Bloch class, extend Bloch c...

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).

Let φ be a holomorphic self-map of the open unit polydisk U in C and p, q > 0. In this paper, the generally weighted Bloch spaces B log(U ) are introduced, and the boundedness and compactness of composition operator Cφ from B p log(U ) to B log(U ) are investigated.

In this short note we provide computational evidence for the main result found in On the Bloch-Kato conjecture for elliptic modular forms of square-free level.

In this paper, we study composition operators Cφf = f ◦ φ, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

CHRISTOPHER J . BISHOP The little Bloch space, 130 , is the space of all holomorphic functions f on the unit disk such that lim1 z 1l (f'(z)j(1 Iz12) = 0. Finite Blaschke products are clearly in 130, but examples of infinite products in 80 are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others) . Stephenson has asked whether 130...

Cancer stem cells (CSCs) form spheres in vitro in serum-free suspension culture. Sphere formation is particularly useful to enrich the potential CSC subpopulations as a functional approach. Few reports are currently available on tumorspheres in esophageal cancer (EC). The present study focused on evaluating the cancer stem-like properties and anal...

Neural stem cells proliferate in liquid culture as cell clusters (neurospheres). This study was undertaken to characterize the epidermal growth factor (EGF)-expanded free-floating neurospheres derived from rat fetal striatum. We examined the ultrastructural and antigenic characteristics of these spheres. They consisted of two cell types, electron-dense and electron-lucent cells. Lucent cells we...