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The hardy-littlewood maximal function of a sobolev function

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Abstract

We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW 1,p(R n) for 1<p≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.

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References

  1. B. Bojarski and P. Hajłlasz,Pointwise inequalities for Sobolev functions and some applications, Studia Mathematica106 (1993), 77–92.

    MATH  MathSciNet  Google Scholar 

  2. H. Federer and W. Ziemer,The Lebesgue set of a function whose distribution derivatives are p-th power summable, Indiana University Mathematics Journal22 (1972), 139–158.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer-Verlag, Berlin, 1983.

    MATH  Google Scholar 

  4. J. L. Lewis,On very weak solutions of certain elliptic systems, Communications in Partial Differential Equations18 (1993), 1515–1537.

    Article  MATH  MathSciNet  Google Scholar 

  5. E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.

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Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland

    Juha Kinnunen

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  1. Juha Kinnunen
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Correspondence to Juha Kinnunen.

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Kinnunen, J. The hardy-littlewood maximal function of a sobolev function. Isr. J. Math. 100, 117–124 (1997). https://doi.org/10.1007/BF02773636

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  • DOI: https://doi.org/10.1007/BF02773636

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