Geodesic
On Density Properties of the Riesz Capacities and the Analytic Capacity $\gamma _+$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 143-156 
P. Mattila; P. V. Paramonov. On Density Properties of the Riesz Capacities and the Analytic Capacity $\gamma _+$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 143-156. http://geodesic.mathdoc.fr/item/TM_2001_235_a9/
@article{TM_2001_235_a9,
     author = {P. Mattila and P. V. Paramonov},
     title = {On {Density} {Properties} of the {Riesz} {Capacities} and the {Analytic} {Capacity~}$\gamma _+$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {143--156},
     year = {2001},
     volume = {235},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_235_a9/}
}
TY  - JOUR
AU  - P. Mattila
AU  - P. V. Paramonov
TI  - On Density Properties of the Riesz Capacities and the Analytic Capacity $\gamma _+$
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2001
SP  - 143
EP  - 156
VL  - 235
UR  - http://geodesic.mathdoc.fr/item/TM_2001_235_a9/
LA  - en
ID  - TM_2001_235_a9
ER  - 
%0 Journal Article
%A P. Mattila
%A P. V. Paramonov
%T On Density Properties of the Riesz Capacities and the Analytic Capacity $\gamma _+$
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2001
%P 143-156
%V 235
%U http://geodesic.mathdoc.fr/item/TM_2001_235_a9/
%G en
%F TM_2001_235_a9

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We prove rather precise results on density properties of the Riesz capacities in $\mathbb R^N$ and the analytic capacity $\gamma _+$ in $\mathbb R^2$.

[1] Carleson L., Selected problems on exceptional sets, Van Nostrand, Princeton, 1966 | MR

[2] Eiderman V. Ya., “Otsenki dlya potentsialov i $\delta$-subgarmonicheskikh funktsii vne isklyuchitelnykh mnozhestv”, Izv. RAN. Ser. mat., 61:6 (1997), 1293–1329 | MR | Zbl

[3] Federer H., Geometric measure theory, Springer-Verl., Berlin, 1969 | MR

[4] Garnett J., Analytic capacity and measure, Lect. Notes Math., 297, Springer-Verl., Berlin, 1972 | MR | Zbl

[5] Mattila P., “An example illustrating integralgeometric measures”, Amer. J. Math., 108 (1986), 693–702 | DOI | MR | Zbl

[6] Mattila P., “On the analytic capacity and curvature of some Cantor sets with non-$\sigma$-finite length”, Publ. Mat., 40 (1996), 195–204 | MR | Zbl

[7] Mattila P., Paramonov P. V., “On geometric properties of harmonic $\mathrm{Lip}_1$-capacity”, Pacif. J. Math., 171:2 (1995), 469–490 | MR

[8] Verdera Dzh., Melnikov M. S., Paramonov P. V., “$C^1$-approksimatsiya i prodolzhenie subgarmonicheskikh funktsii”, Mat. sb., 192:4 (2001), 37–58 | MR | Zbl

[9] Tolsa X., “$L^2$-boundedness of the Cauchy integral operator for continuous measures”, Duke Math. J., 98:2 (1999), 269–304 | DOI | MR | Zbl

[10] Vitushkin A. G., “Analiticheskaya emkost mnozhestv v zadachakh teorii priblizhenii”, UMN, 22:6 (1967), 141–199 | MR