Interpolation for Hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales
 作者： Paul F. X. Müller,  Peter Yuditskii 作者单位： 1Institut für Analysis J. Kepler Universität Linz A-4040 Linz, Austria2Institut 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.

• 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