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Bounded Operators on Mixed Norm Lebesgue Spaces

  • Nikita Evseev
  • Alexander Menovschikov
Article
  • 32 Downloads

Abstract

We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given (in the case when the inducing mapping preserve the priority of variables). For a certain class of integral operators, we provide sufficient conditions for boundedness. We conclude by applying the developed technique to the investigation of Hardy–Steklov type operators.

Keywords

Mixed norm Lebesgue spaces Composition operator Hardy operator 

Mathematics Subject Classification

Primary 47B33 Secondary 47G10 

Notes

Acknowledgements

Authors gratefully acknowledge the guidance of Prof. Vodopyanov and wish to thank Prof. Jain for bringing the theory of mixed norm spaces to their attention. We are also grateful to the referees for their constructive input.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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