Multipliers in Holomorphic Mean Lipschitz Spaces on the Unit Ball

Abstract

For $1\le p\le \infty$ and $s>\mathrm{0,}$ let ${\Lambda }_s^p$ be holomorphic mean Lipschitz spaces on the unit ball in ${ℂ}^n$. It is shown that, if $s>n/\mathrm{p,}$ the space ${\Lambda }_s^p$ is a multiplicative algebra. If $s>n/p$, then the space ${\Lambda }_s^p$ is not a multiplicative algebra. We give some sufficient conditions for a holomorphic function to be a pointwise multiplier of ${\Lambda }_{n/p}^p$.