Distance of a Bloch Function to the Little Bloch Space

Abstract

Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β 0 . Immediate consequences are equivalent expressions for functions in β 0 . We also give several examples of distances of specific functions to β 0 . We comment on connections between distance to β 0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.