Absolutely summing multipliers on abstract Hardy spaces
The authors, motivated by the study of multipliers \((H^p, \ell^q)\) from \(H^p\) into \(\ell^q\) which are \(1\)-summing and \(2\)-summing due to \textit{I. Almasri} [J. Math. Anal. Appl. 237, No.~2, 451--463 (1999; Zbl 0945.47023)], analyse similar questions for multipliers \((HX, E)\) from abstract Hardy spaces \(HX\) consisting of functions holomorphic in the disc such that \(\sup_r \|f_r\|_X<\infty\) for a given complex symmetric space \(X\) defined in \(\mathbb T\) into a Banach sequence lattice \(E\). The paper combines tools from interpolation theory and some general facts from the theory of absolutely summing operators and Banach lattices together with the use of the Hausdorff-Young inequality \(\|(\hat f(n))\|_E\leq C \|f\|_{HX}\), and some inequalities concerning Taylor coefficients of functions in Hardy-Orlicz spaces.
scientific article; zbMATH DE number 5629545
scientific article