Pointwise multipliers on the weighted BMOA space

Abstract

Let = {z : |z| < 1} be the unit disk in the complex plane C, Φ : → C is a analytic map. We study the multiplication operator M Φ on the logarithmic weighted BMOA space . We obtain that a sufficient condition for the operator M Φ to be a bounded operator on BMOA log. We also get that another necessary condition for the operator M Φ to be bounded on BMOA log.