On a decomposition of non-negative Radon measures

Bérenger Akon Kpata

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 4, page 203-210
  • ISSN: 0044-8753

Abstract

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We establish a decomposition of non-negative Radon measures on d which extends that obtained by Strichartz [6] in the setting of α -dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.

How to cite

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Kpata, Bérenger Akon. "On a decomposition of non-negative Radon measures." Archivum Mathematicum 055.4 (2019): 203-210. <http://eudml.org/doc/294346>.

@article{Kpata2019,
abstract = {We establish a decomposition of non-negative Radon measures on $\mathbb \{R\}^\{d\}$ which extends that obtained by Strichartz [6] in the setting of $\alpha $-dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.},
author = {Kpata, Bérenger Akon},
journal = {Archivum Mathematicum},
keywords = {Bessel capacity; fractional maximal operator; Hausdorff measure; non-negative Radon measure; Riesz potential},
language = {eng},
number = {4},
pages = {203-210},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On a decomposition of non-negative Radon measures},
url = {http://eudml.org/doc/294346},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Kpata, Bérenger Akon
TI - On a decomposition of non-negative Radon measures
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 4
SP - 203
EP - 210
AB - We establish a decomposition of non-negative Radon measures on $\mathbb {R}^{d}$ which extends that obtained by Strichartz [6] in the setting of $\alpha $-dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.
LA - eng
KW - Bessel capacity; fractional maximal operator; Hausdorff measure; non-negative Radon measure; Riesz potential
UR - http://eudml.org/doc/294346
ER -

References

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  1. Adams, D.R., Hedberg, L.I., Function spaces and potential theory, Grundlehren der mathematischen Wissenschaften, vol. 314, Springer-Verlag, London-Berlin-Heidelberg-New York, 1996. (1996) MR1411441
  2. Dal Maso, G., On the integral representation of certain local functionals, Ric. Mat. 32 (1) (1983), 85–113. (1983) MR0740203
  3. Falconner, K.J., Fractal geometry, Wiley, New York, 1990. (1990) MR1102677
  4. Molter, U.M., Zuberman, L., 10.14321/realanalexch.34.1.0069, Real Anal. Exchange 34 (1) (2008/2009), 69–86. (2008) MR2527123DOI10.14321/realanalexch.34.1.0069
  5. Phuc, N.C., Torrès, M., 10.1512/iumj.2008.57.3312, Indiana Univ. Math. J. 57 (4) (2008), 1573–1597. (2008) MR2440874DOI10.1512/iumj.2008.57.3312
  6. Strichartz, R.S., 10.1016/0022-1236(90)90009-A, J. Funct. Anal. 89 (1990), 154–187. (1990) MR1040961DOI10.1016/0022-1236(90)90009-A
  7. Véron, L., Elliptic equations involving measures, Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 1, 2004, pp. 593–712. (2004) 
  8. Ziemer, W.P., Weakly Differentiable Functions, Springer-Verlag, New York, 1989. (1989) Zbl0692.46022MR1014685

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