Multipliers of Hardy spaces (Q2732382)

Let \(X\) and \(Y\) be two vector spaces of sequences. A sequence \(\lambda= \{\lambda_n\}\) is said to be a multiplier from \(X\) to \(Y\), if \(\{\lambda_n x_n\}\in Y\) whenever \(\{x_n\}\in X\). The set of all multipliers from \(X\) to \(Y\) will be denoted by \((X,Y)\). We regard spaces of analytic functions in the open unit disc \(D\) as sequence space by identifying a function with its sequence of Taylor coefficients. \(H^p\), \(0<p\leq\infty\) denote the usual Hardy spaces on \(D\) and \(B\) denotes the Bloch space on \(D\). The author describes \((H^p,B)\) for \(1<p\leq \infty\) generalizing \((H^1,B)=B\). Moreover he shows (BMOA, \(H^q)=\ell^\infty\) for \(1\leq q\leq \infty\).