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Multipliers and Lp-operator Semigroups

  • Werner J. RickerEmail author
Conference paper
  • 445 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 240)

Abstract

Deciding whether the generator of certain semigroups of operators in \( \mathit{L^p} \)(R) are unbounded scalar-type spectral operators can be reduced to deciding when \( {e^{i\varphi }} \), for specific unbounded functions \( \varphi :\mathbb{R} \to \mathbb{R} \), is a p-multiplier. We illustrate how van der Corput’s lemma is an effective technique in this regard.

Keywords

Operator semigroup p-multiplier van der Corput lemma volume doubling Hardy–Littlewood maximal operator 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Math.-Geogr. FakultätKatholische Universität Eichstätt-IngolstadtEichstättGermany

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