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Restrictions of Riesz–Morrey potentials

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Arkiv för Matematik

Abstract

This paper is devoted to exploiting the restrictions of Riesz–Morrey potentials on either unbounded or bounded domains in Euclidean spaces.

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References

  1. Adams, D. R., Traces of potentials arising from translation invariant operators, Ann. Sc. Norm. Sup. Pisa 25 (1971), 203–217. (Classe di Sci. 3e série)

    MathSciNet  MATH  Google Scholar 

  2. Adams, D. R., A note on Riesz potentials, Duke Math. J. 42 (1975), 765–778.

    Article  MathSciNet  MATH  Google Scholar 

  3. Adams, D. R., Weighted nonlinear potential theory, Trans. Amer. Math. Soc. 297 (1986), 73–94.

    Article  MathSciNet  MATH  Google Scholar 

  4. Adams, D. R., A sharp inequality of J. Moser for higher order derivatives, Ann. Math. (2) 128 (1988), 385–398.

    Article  MathSciNet  MATH  Google Scholar 

  5. Adams, D. R. and Hedberg, L. I., Function Spaces and Potential Theory, Springer, Berlin, 1996.

    Book  MATH  Google Scholar 

  6. Adams, D. R. and Meyers, N. G., Thinness and Wiener criteria for non-linear potentials, Indiana Univ. Math. J. 22 (1972), 169–197.

    Article  MathSciNet  MATH  Google Scholar 

  7. Adams, D. R. and Xiao, J., Nonlinear analysis on Morrey spaces and their capacities, Indiana Univ. Math. J. 53 (2004), 1629–1663.

    Article  MathSciNet  MATH  Google Scholar 

  8. Adams, D. R. and Xiao, J., Morrey spaces in harmonic analysis, Ark. Mat. 50 (2012), 201–230.

    Article  MathSciNet  MATH  Google Scholar 

  9. Adams, D. R. and Xiao, J., Morrey potentials and harmonic maps, Comm. Math. Phys. 308 (2011), 439–456. Erratum, Comm. Math. Phys. 339 (2015), 769–771.

    Article  MathSciNet  MATH  Google Scholar 

  10. Adams, D. R. and Xiao, J., Regularity of Morrey commutators, Trans. Amer. Math. Soc. 364 (2012), 4801–4818.

    Article  MathSciNet  MATH  Google Scholar 

  11. Adams, D. R. and Xiao, J., Singularities of nonlinear elliptic systems, Comm. Partial Diff. Equ. 38 (2013), 1256–1273.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.

    MATH  Google Scholar 

  13. Hedberg, L. I. and Wolff, Th. H., Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble) 33 (1983), 161–187.

    Article  MathSciNet  MATH  Google Scholar 

  14. Lieb, E. H. and Loss, M., Analysis, 2nd ed., GSM 14, Am. Math. Soc., Providence, 2001.

    MATH  Google Scholar 

  15. Lu, Y., Yang, D. and Yuan, W., Interpolation of Morrey spaces on metric measure spaces, Canad. Math. Bull. 57 (2014), 598–608.

    Article  MathSciNet  MATH  Google Scholar 

  16. Malý, J. and Ziemer, W. P., Fine Regularity of Solutions of Elliptic Partial Differential Equations, Mathematical Surveys and Monographs 51, Am. Math. Soc., Providence, 1997.

    MATH  Google Scholar 

  17. Muckenhoupt, B. and Wheeden, R., Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261–274.

    Article  MathSciNet  MATH  Google Scholar 

  18. Serrin, J., A remark on the Morrey potential, Contemp. Math. 426 (2007), 307–315.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Jie Xiao.

Additional information

J. Xiao is in part supported by NSERC of Canada.

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Adams, D.R., Xiao, J. Restrictions of Riesz–Morrey potentials. Ark Mat 54, 201–231 (2016). https://doi.org/10.1007/s11512-016-0238-2

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  • DOI: https://doi.org/10.1007/s11512-016-0238-2

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