Absolutely summing multipliers on abstract Hardy spaces
type: Item
instance of: scholarly article
title: Absolutely summing multipliers on abstract Hardy spaces
zbMATH Open document ID: 1191.46022
author: Paweł Mleczko
author: Mieczysław Mastyło
publication date: 2009-11-11T00:00:00Z
review text: 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.
reviewed by: Oscar Blasco
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 42A45
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 5629545
zbMATH Keywords: Hardy-Orlicz spaces
zbMATH Keywords: multipliers
zbMATH Keywords: interpolation spaces
zbMATH Keywords: Banach lattices
MaRDI profile type: Publication
full work available at URL: s10114-009-7407-1
OpenAlex ID: W2033919692
cites work: Absolutely summing multipliers on \(H^p\) spaces
cites work: Q4188284
cites work: An \(H^ 1\) multiplier theorem
cites work: Multipliers of Hardy Spaces
cites work: Q4039801
cites work: Q4087497
cites work: Q4850055
cites work: Q3772707
cites work: Notes on interpolation of Hardy spaces
cites work: Q3254471
cites work: Summing inclusion maps between symmetric sequence spaces, a survey
cites work: A factorization theorem in Banach lattices and its application to Lorentz spaces
cites work: Hilbertian and complemented finite-dimensional subspaces of Banach lattices and unitary ideals
cites work: On a theorem of L. Schwartz and its applications to absolutely summing operators
cites work: Q4722695
cites work: On the Multipliers of H p Spaces
cites work: Orlicz spaces and modular spaces
cites work: Operational Bezoutiant in the theory of separation of roots of entire functions
cites work: On linear functionals in Hardy-Orlicz spaces, II
cites work: Q3709338
cites work: Diagonal mappings between sequence spaces
DOI: 10.1007/S10114-009-7407-1
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629545