Multipliers in Holomorphic Mean Lipschitz Spaces on the Unit Ball

Abstract

For 1≤p≤∞ and s>0, let Λsp be holomorphic mean Lipschitz spaces on the unit ball in ℂn. It is shown that, if s>n/p, the space Λsp is a multiplicative algebra. If s>n/p, then the space Λsp is not a multiplicative algebra. We give some sufficient conditions for a holomorphic function to be a pointwise multiplier of Λn/pp.