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CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS

Part of: Miscellaneous topics of analysis in the complex domain Normed linear spaces and Banach spaces; Banach lattices Spaces and algebras of analytic functions

Published online by Cambridge University Press:  29 March 2021

Mikael Lindström Open the ORCID record for Mikael Lindström [Opens in a new window] ,
Mieczysław Mastyło Open the ORCID record for Mieczysław Mastyło [Opens in a new window] ,
Paweł Mleczko Open the ORCID record for Paweł Mleczko [Opens in a new window] ,
David Norrbo Open the ORCID record for David Norrbo [Opens in a new window]  and
Michał Rzeczkowski Open the ORCID record for Michał Rzeczkowski [Opens in a new window]
Mikael Lindström
Affiliation:
Department of Mathematics, Åbo Akademi University, FI-20500 Åbo, Finland (mikael.lindstrom@abo.fi)
Mieczysław Mastyło
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University Poznań, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland (mastylo@amu.edu.pl)
Paweł Mleczko
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University Poznań, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland (pml@amu.edu.pl)
David Norrbo
Affiliation:
Department of Mathematics, Åbo Akademi University, FI-20500 Åbo, Finland (dnorrbo@abo.fi)
Michał Rzeczkowski
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University Poznań, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland (rzeczkow@amu.edu.pl)
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Abstract

This paper presents an approach, based on interpolation theory of operators, to the study of interpolating sequences for interpolation Banach spaces between Hardy spaces. It is shown that the famous Carleson result for H∞ can be lifted to a large class of abstract Hardy spaces. A description is provided of the range of the Carleson operator defined on interpolation spaces between the classical Hardy spaces in terms of uniformly separated sequences. A key role in this description is played by some general interpolation results proved in the paper. As by-products, novel results are obtained which extend the Shapiro–Shields result on the characterisation of interpolation sequences for the classical Hardy spaces Hp. Applications to Hardy–Lorentz, Hardy–Marcinkiewicz and Hardy–Orlicz spaces are presented.

Keywords

Carleson interpolating sequencesinterpolation of operatorsHardy spaces

MSC classification

Primary: 30E05: Moment problems, interpolation problems
Secondary: 46B70: Interpolation between normed linear spaces 30H10: Hardy spaces
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 6 , November 2022 , pp. 1915 - 1945
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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