Solutions of Second Order Complex Differential Equation Having Certain Pre-given Zeros

For 0 < s < 1, let . D be a separated sequence such that zn. (1-|zn|)sdzn is an s-Carleson measure. In this paper, we show that there exist certain analytic functions A such that the second order complex differential equation f + Af = 0 admits a non-trivial solution f whose zero-sequence is , where the solution f belongs to some Mobius invariant function spaces. We strengthen a previous result from the literature.