On the interpolation constants for variable Lebesgue spaces

Oleksiy Karlovych, Eugene Shargorodsky

Research output: Contribution to journalArticlepeer-review


For (Formula presented.) and variable exponents (Formula presented.) and (Formula presented.) with values in [1, ∞], let the variable exponents (Formula presented.) be defined by (Formula presented.) The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space (Formula presented.) to the variable Lebesgue space (Formula presented.) for (Formula presented.), then (Formula presented.) where C is an interpolation constant independent of T. We consider two different modulars (Formula presented.) and (Formula presented.) generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that (Formula presented.) and (Formula presented.), as well as, lead to sufficient conditions for (Formula presented.) and (Formula presented.). We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that (Formula presented.), (Formula presented.) are Lipschitz continuous and bounded away from one and infinity (in this case, (Formula presented.)).

Original languageEnglish
Pages (from-to)2877-2902
Number of pages26
JournalMathematische Nachrichten
Issue number7
Publication statusPublished - Jul 2023


  • Calderón product
  • complex method of interpolation
  • interpolation constant
  • Riesz–Thorin interpolation theorem
  • variable Lebesgue space


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