ON THE p-NORM OF THE BEREZIN TRANSFORM

摘要

In this short note, the norm of Berezin transform, acting on L~p(B_n), is determined to be ‖B_B_n:L~p(B_n)→L~p‖=1/p∏_(k=1)~n(1+1/kp)π/sin(π/p). This extends a result of Dostanic (J. Anal. Math. 104 (2008) 13-23) to several complex variables.