Real Analysis pp 221-274 | Cite as

The Lp(E) Spaces

  • Emmanuele DiBenedetto
Part of the Birkhäuser Advanced Texts book series (BAT)

Abstract

Let { X,A,μ} be a measure space and let E be a measurable subset of X. A measurable function \(f:E \to {{\mathbb{R}}^{*}}\) is said to be in L P (E) for P≥1 if is integrable on E, i.e., if
$$ \left\| f \right\|_p \mathop = \limits^{def} \left( {\smallint _E \left| f \right|^p d\mu } \right)^{1/p} < \infty $$
(1.1)p

Keywords

Convolution Radon 

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Emmanuele DiBenedetto
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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