Atomic Hp spaces

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


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


Banach Space Orthonormal Basis Unit Disc Convergence Theorem Algebraic Geometry 
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© Springer Japan 2001

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  • Akihito Uchiyama

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