Spaces Lp and Convolutions

  • Adriaan C. Zaanen
Part of the Universitext book series (UTX)


Before discussing an important special class of measurable functions we prove a fundamental inequality, known as Hölder’s inequality. There are two variants, one for sums and one for integrals. The original variant for integrals of continuous functions or Riemann integrable functions was extended to measurable functions without additional difficulties.


Lebesgue Measure Step Function Differentiable Function Triangle Inequality Cauchy Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Adriaan C. Zaanen
    • 1
  1. 1.Department of MathematicsUniversity of LeidenLeidenThe Netherlands

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