Coefficient multipliers of mixed norm space in the ball
The authors use the Hadamard method and the general D-dual method of \textit{J.\,M.\thinspace Anderson} and \textit{A.\,L.\thinspace Shields} [Trans.\ Am.\ Math.\ Soc.\ 224, 255--265 (1977; Zbl 0352.30032)], respectively, to characterize the coefficient multiplier spaces of mixed norm spaces \((H_{p,q}(\phi_1),H_{u,v}(\phi_2))\) in the unit ball for the values of \(p,q,u,v\) in three cases: (i) \(0<p\leq u\leq \infty\), \(0<q\leq \min(1,v)\leq \infty.\) (ii) \(v=\infty\), \(0<p\leq u\leq \infty\), \(1\leq u,q\leq \infty\). (iii) \(1\leq v\leq 2\leq q\leq \infty\), and \(0<p\leq u\leq \infty\) or \(1\leq p,u\leq \infty\). The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
scientific article; zbMATH DE number 5127973
scientific article