Interpolation for hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales

Paul F.X. Müller, Peter Yuditskii

Research output: Contribution to journalArticlepeer-review

Abstract

The real and complex interpolation spaces for the classical Hardy spaces H1 and H∞ were determined in 1983 by P. W. Jones. Due to the analytic constraints the associated Marcinkiewicz decomposition gives rise to a delicate approximation problem for the L1 metric. Specifically for f ε Hp the size of (formula presented) needs to be determined for any λ ε R+: In the present paper we develop a new set of truncation formulae in order to obtain the Marcinkiewicz decomposition of (H1, H∞). We revisit the real and complex interpolation theory for Hardy spaces by examining our newly found formulae.

Original languageEnglish
Pages (from-to)141-155
Number of pages15
JournalColloquium Mathematicum
Volume158
Issue number1
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2019.

Keywords

  • Complex and real interpolation spaces
  • Hardy spaces
  • Holomorphic martingales
  • Marcinkiewicz decomposition

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