The converse of the Fatou theorem for smooth measures
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 90-95 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We prove the converse of the Fatou theorem for small Zygmund measures defined on the Euclidean space.
@article{ZNSL_2004_315_a5,
     author = {E. Doubtsov},
     title = {The converse of the {Fatou} theorem for smooth measures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {90--95},
     year = {2004},
     volume = {315},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/}
}
TY  - JOUR
AU  - E. Doubtsov
TI  - The converse of the Fatou theorem for smooth measures
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 90
EP  - 95
VL  - 315
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/
LA  - ru
ID  - ZNSL_2004_315_a5
ER  - 
%0 Journal Article
%A E. Doubtsov
%T The converse of the Fatou theorem for smooth measures
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 90-95
%V 315
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/
%G ru
%F ZNSL_2004_315_a5
E. Doubtsov. The converse of the Fatou theorem for smooth measures. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 90-95. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a5/

[1] J. Brossard, L. Chevalier, “Problème de Fatou ponctuel et dérivabilité des mesures”, Acta Math., 164:3–4 (1990), 237–263 | DOI | MR | Zbl

[2] J. J. Carmona, J. J. Donaire, “The converse of Fatou's theorem for Zygmund measures”, Pacific J. Math., 191:2 (1999), 207–222 | DOI | MR | Zbl

[3] E. Doubtsov, A. Nicolau, “Symmetric and Zygmund measures in several variables”, Ann. Inst. Fourier (Grenoble), 52:1 (2002), 153–177 | MR | Zbl

[4] L. H. Loomis, “The converse of the Fatou theorem for positive harmonic functions”, Trans. Amer. Math. Soc., 53 (1943), 239–250 | DOI | MR | Zbl

[5] W. Rudin, “Tauberian theorems for positive harmonic functions”, Nederl. Akad. Wetensch. Indag. Math., 40:3 (1978), 376–384 | MR