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article · Journal of the Institute of Mathematics of Jussieu · 2021

CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS

Mikael Lindström, Mieczysław Mastyło, Paweł Mleczko, David Norrbo, Michał Rzeczkowski

Cited by 1Open access

Abstract

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 forH∞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 spacesHp. Applications to Hardy–Lorentz, Hardy–Marcinkiewicz and Hardy–Orlicz spaces are presented.

Cite this paper

APA 7

Lindström, M., Mastyło, M., Mleczko, P., Norrbo, D., & Rzeczkowski, M. (2021). CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS. Journal of the Institute of Mathematics of Jussieu, 21(6), 1915–1945. https://doi.org/10.1017/s1474748021000049

MLA 9

Lindström, Mikael, et al. “CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS.” Journal of the Institute of Mathematics of Jussieu, vol. 21, no. 6, 2021, pp. 1915–45, https://doi.org/10.1017/s1474748021000049.

Chicago

Lindström, Mikael, Mieczysław Mastyło, Paweł Mleczko, David Norrbo, and Michał Rzeczkowski. 2021. “CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS.” Journal of the Institute of Mathematics of Jussieu 21 (6): 1915–45. https://doi.org/10.1017/s1474748021000049.

Harvard

Lindström, M. et al. (2021) ‘CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS’, Journal of the Institute of Mathematics of Jussieu, 21(6), pp. 1915–1945. Available at: https://doi.org/10.1017/s1474748021000049.

BibTeX
@article{lindstrom2021carleson,
  title = {{CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS}},
  author = {Lindström, Mikael and Mastyło, Mieczysław and Mleczko, Paweł and Norrbo, David and Rzeczkowski, Michał},
  journal = {Journal of the Institute of Mathematics of Jussieu},
  volume = {21},
  number = {6},
  pages = {1915--1945},
  year = {2021},
  doi = {10.1017/s1474748021000049}
}

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