Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic selfmap of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗ (U) ) and Bq(...

Let Un be the unit polydisc of Cn and φ = (φ1, . . . ,φn) a holomorphic self-map of Un. p(Un), p 0 (U n), and p 0∗(U n) denote the p-Bloch space, little p-Bloch space, and little star p-Bloch space in the unit polydisc Un, respectively, where p,q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between p(Un) ( p 0 (U n) or p 0∗(U n)) an...

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).

Liouville's theorem on the conservation of phase-space volume is violated by Berry phase in the semiclassical dynamics of Bloch electrons. This leads to a modification of the phase-space density of states, whose significance is discussed in a number of examples: field modification of the Fermi-sea volume, connection to the anomalous Hall effect, and a general formula for orbital magnetization. ...

Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic self-map of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗(Un) ) and Bq...