| Title:
|
On a decomposition of non-negative Radon measures (English) |
| Author:
|
Kpata, Bérenger Akon |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
203-210 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Bessel capacity |
| Keyword:
|
fractional maximal operator |
| Keyword:
|
Hausdorff measure |
| Keyword:
|
non-negative Radon measure |
| Keyword:
|
Riesz potential |
| MSC:
|
28A12 |
| MSC:
|
28A33 |
| MSC:
|
28A78 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 07144735 |
| idMR:
|
MR4038355 |
| DOI:
|
10.5817/AM2019-4-203 |
| . |
| Date available:
|
2019-10-30T08:49:50Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147872 |
| . |
| Reference:
|
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| Reference:
|
[2] Dal Maso, G.: On the integral representation of certain local functionals.Ric. Mat. 32 (1) (1983), 85–113. MR 0740203 |
| Reference:
|
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| Reference:
|
[4] Molter, U.M., Zuberman, L.: A fractal Plancherel theorem.Real Anal. Exchange 34 (1) (2008/2009), 69–86. MR 2527123, 10.14321/realanalexch.34.1.0069 |
| Reference:
|
[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. MR 2440874, 10.1512/iumj.2008.57.3312 |
| Reference:
|
[6] Strichartz, R.S.: Fourier asymptotics of fractal measures.J. Funct. Anal. 89 (1990), 154–187. MR 1040961, 10.1016/0022-1236(90)90009-A |
| Reference:
|
[7] Véron, L.: Elliptic equations involving measures.Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 1, 2004, pp. 593–712. MR 2103694 |
| Reference:
|
[8] Ziemer, W.P.: Weakly Differentiable Functions.Springer-Verlag, New York, 1989. Zbl 0692.46022, MR 1014685 |
| . |
