On the coefficient multipliers of a space of analytic functions on the unit disc

Abstract

B(α), α>0, is defined as the normed linear space of all analytic functions f in the unit disc for which $$ \parallel{f} \parallel_{\alpha} = \sup_{\mid z \mid<1} (1- \mid z \mid}^{α} \mid f``(z) \mid<∞$$ The class B(1) of Bloch functions has been extensively studied. We want to make a study on B(α) which is parallel to that of B(1). Especially, we calculate the dual space of B(α) and the multipliers to the mixed norm sequence space ℓ(p,q) by means of the fractional integral and differential operators.