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Variants of the Inequalities of Paley and Zygmund

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Abstract

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

Keywords

Lacunary Fourier series Paley’s inequality Zygmund’s inequality Multiplier inclusion 

Mathematics Subject Classification

Primary 43A46 42A55 42A45 

Notes

Acknowledgements

This work was conducted during the author’s Ph.D. studies at the University of Edinburgh under the supervision of Professor Jim Wright. The author would like to thank and acknowledge his Ph.D. supervisor for his continuous help, support and guidance on this work and for all his useful comments and suggestions that improved the presentation of this paper.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Department of MathematicsStockholm UniversityStockholmSweden

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