On multipliers from spaces of the Bergman type to the Hardy spaces in a polydisk (Q2730513)

The author describes coefficient multipliers of the Taylor series acting from the space of holomorphic functions on a polydisk \(U^n\) with the norm NEWLINE\[NEWLINE \|f\|=\left\{ \int_{T^n}\left( \int_{I^n}|f(R\xi)|^q(1- R)^{\alpha q-1}dR\right)^{p/q}dm_n(\xi)\right\}^{1/p}, NEWLINE\]NEWLINE where \(T^n\) is the skeleton of the polydisk, \(I=(0,1)\), \(0<p,q\leq 1\), \(0<\alpha <\infty\), \(m_n\) is the Lebesgue measure on \(T^n\), to the Hardy space \(H^s(U^n)\), \(\max (p,q)\leq s\leq 1\).