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A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n

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Abstract

We show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝn in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small order.

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Authors and Affiliations

  1. Universidade do Algarve Campus de Gambelas, Faro, 8005, Portugal

    Stefan Samko

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  1. Stefan Samko
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Correspondence to Stefan Samko.

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Dedicated to Professor Francesco Mainardi on the occasion of his 70th anniversary

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Samko, S. A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n . fcaa 16, 370–377 (2013). https://doi.org/10.2478/s13540-013-0023-x

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  • DOI: https://doi.org/10.2478/s13540-013-0023-x

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