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Atomic Hp spaces

  • Akihito Uchiyama
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

Definition 2.1. For p ∈ (0,1] and for fD let
$$ \begin{array}{l} \left\| f \right\|_{H^P } = {\rm{inf }}\left\{ {\left\| {\left\{ {{\rm{\lambda }}_j } \right\}} \right.} \right\}\left\| {_{\ell ^p } :{\rm{ there exists a sequence of (}}p,\infty {\rm{)}}} \right. - {\rm{atoms}} \\ {\rm{ }}\left\{ {a_j \left( x \right)} \right\}_{j \in {\rm{N}}} {\rm{ such that}} \\ {\rm{ }}f{\rm{ = }}\mathop {\lim }\limits_{m \to \infty ^{{\rm{in}}D'} } \sum\limits_{j = 1}^m {\lambda _j } a_j \} \\ {\rm{where inf \theta = }}\infty {\rm{. Let}} \\ {\rm{ }}H^p = \left\{ {f \in D':\left\| f \right\|_{H^p } < \infty } \right\}. \\ \end{array} $$
(2.1)

Keywords

Banach Space Orthonormal Basis Unit Disc Convergence Theorem Algebraic Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Akihito Uchiyama

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