TY - JOUR

T1 - Clark measures on the complex sphere

AU - Aleksandrov, Aleksei B.

AU - Doubtsov, Evgueni

N1 - Publisher Copyright: © 2019 Elsevier Inc.

PY - 2020/1/15

Y1 - 2020/1/15

N2 - Let Bd denote the unit ball of Cd, d≥1. Given a holomorphic function φ:Bd→B1, we study the corresponding family σα[φ], α∈∂B1, of Clark measures on the unit sphere ∂Bd. If φ is an inner function, then we introduce and investigate related unitary operators Uα mapping analogs of model spaces onto L2(σα), α∈∂B1. In particular, we explicitly characterize the set of Uα ⁎f such that fσα is a pluriharmonic measure. Also, for an arbitrary holomorphic φ:Bd→B1, we use the family σα[φ] to compute the essential norm of the composition operator Cφ:H2(B1)→H2(Bd).

AB - Let Bd denote the unit ball of Cd, d≥1. Given a holomorphic function φ:Bd→B1, we study the corresponding family σα[φ], α∈∂B1, of Clark measures on the unit sphere ∂Bd. If φ is an inner function, then we introduce and investigate related unitary operators Uα mapping analogs of model spaces onto L2(σα), α∈∂B1. In particular, we explicitly characterize the set of Uα ⁎f such that fσα is a pluriharmonic measure. Also, for an arbitrary holomorphic φ:Bd→B1, we use the family σα[φ] to compute the essential norm of the composition operator Cφ:H2(B1)→H2(Bd).

KW - Composition operator

KW - Hardy space

KW - Inner function

KW - Pluriharmonic measure

UR - http://www.scopus.com/inward/record.url?scp=85072701355&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2019.108314

DO - 10.1016/j.jfa.2019.108314

M3 - Article

AN - SCOPUS:85072701355

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

M1 - 108314

ER -