Interpolation for Hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales
作者: Paul F. X. MüllerPeter Yuditskii
作者单位: 1Institut für Analysis J. Kepler Universität Linz A-4040 Linz, Austria
2Institut für Analysis Abteilung für Dynamische Systeme und Approximationstheorie J. Kepler Universität Linz A-4040 Linz, Austria
刊名: Colloquium Mathematicum, 2019, Vol.158 , pp.141-155
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/cm7460-10-2018
原始语种摘要: The real and complex interpolation spaces for the classical Hardy spaces $H^1$ and $H^\infty$ 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 $L^ 1$ metric.Specifically for $ f \in H^p$ the size of $$ {\rm{inf}} \{ \| f - f_1 \| _1 : f_1 \in H^\infty ,\, \|f_1\|_\infty \le \lambda \}$$ needs to be determined for any $\lambda \in \mathbb R_+. $ In the present paper we develop a new set of truncation formulae in order to obtain the Marcinkiewicz decomposition of $(H^1, H^\infty) $. We revisit the real and complex interpolation theory for Hardy spaces by examining our newly found formulae.
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  • decomposition 分解
  • interpolation 内插法
  • complex 超群
  • lambda 朗达海洋水文定位系统
  • formulae 公式
  • analytic 解析的
  • develop 发展
  • truncation 
  • problem 题目
  • revisit 再访问