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Mathematical Notes

, Volume 105, Issue 1–2, pp 91–103 | Cite as

Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis

  • V. D. StepanovEmail author
  • E. P. UshakovaEmail author
Article
  • 6 Downloads

Abstract

Estimates of the norms of spaces associated to weighted first-order Sobolev spaces with various weight functions and summation parameters are established. As the main technical tool, boundedness criteria for the Hardy–Steklov integral operator with variable limits of integration in Lebesgue spaces on the real axis are used.

Keywords

Sobolev space Hardy–Steklov operator duality principle 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Computing Center of Far-Eastern Branch of Russian Academy of SciencesKhabarovskRussia

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