Previous |  Up |  Next

Article

Keywords:
Bessel capacity; fractional maximal operator; Hausdorff measure; non-negative Radon measure; Riesz potential
Summary:
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.
References:
[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. MR 1411441
[2] Dal Maso, G.: On the integral representation of certain local functionals. Ric. Mat. 32 (1) (1983), 85–113. MR 0740203
[3] Falconner, K.J.: Fractal geometry. Wiley, New York, 1990. MR 1102677
[4] Molter, U.M., Zuberman, L.: A fractal Plancherel theorem. Real Anal. Exchange 34 (1) (2008/2009), 69–86. DOI 10.14321/realanalexch.34.1.0069 | MR 2527123
[5] Phuc, N.C., Torrès, M.: Characterizations of the existence and removable singularities of divergence-measure vector fields. Indiana Univ. Math. J. 57 (4) (2008), 1573–1597. DOI 10.1512/iumj.2008.57.3312 | MR 2440874
[6] Strichartz, R.S.: Fourier asymptotics of fractal measures. J. Funct. Anal. 89 (1990), 154–187. DOI 10.1016/0022-1236(90)90009-A | MR 1040961
[7] Véron, L.: Elliptic equations involving measures. Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 1, 2004, pp. 593–712.
[8] Ziemer, W.P.: Weakly Differentiable Functions. Springer-Verlag, New York, 1989. MR 1014685 | Zbl 0692.46022
Partner of
EuDML logo