On a decomposition of non-negative Radon measures

Bérenger Akon Kpata

Address: Laboratoire de Mathématiques et Informatique, UFR des Sciences Fondamentales et Appliquées, Université Nangui Abrogoua, 02 BP 801 Abidjan 02, Côte d’Ivoire

E-mail: kpata_akon@yahoo.fr

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.

AMSclassification: primary 28A33; secondary 28A78, 28A12, 42B25.

Keywords: Bessel capacity, fractional maximal operator, Hausdorff measure, non-negative Radon measure, Riesz potential.

DOI: 10.5817/AM2019-4-203