On characterizations of isometries on function spaces

Abstract

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball Bn in C n .

Remarks on two theorems of Qi-Keng Lu

“…Finally we must mention that some interesting work due to Li [12] on the characterization of Euclidean ball was reported at the Beijing conference in honor of Qi-Keng Lu in June, 2006. The lecture and survey article of Weiping Yin [13] is one of the motivations for us to write this article dedicated to Qi-Keng Lu.…”

Isometric composition operators on weighted Dirichlet-type spaces

“…In [3] The isometric composition operators on the Bloch spaces in the unit disk were discussed by Martín and Vukotić [7], Colonna [8], Allen and Colonna [9,10], Li and Zhou [11]. The same problems were studied on the Bloch spaces in the unit polydisk by Cohen and Colonna [12], in unit ball by Li [13], and Li and Ruan [14]. For the BMOA space, see [15].…”

Some isometric operators on the Dirichlet space

“…The isometric composition operators on the Bloch spaces in the unit disk were discussed by Martín and Vukotić in [14], Colonna in [3], Allen and Colonna in [1, 2], Li and Zhou in [11]. The same problems were studied on the Bloch spaces in the unit polydisk by Cohen and Colonna in [4], in unit ball by Li et al in [9,10]. For the BMOA space, to see [8].…”