no. 3
Convergence on almost every line for functions with gradient in L p (𝐑 n )
Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 159-164.

On démontre que si grad (f)∈L p (R n ) pour certaines valeurs de p, alors

lim x 1 → ∞ f ( x 1 , x 2 , ... , x n ) = const., p.p. dans R n - 1 .

We prove that if grad (f)∈L p (R n ) for certain values of p, then

lim x 1 → ∞ f ( x 1 , x 2 , ... , x n ) = const., a.e. in R n - 1 . 

@article{AIF_1974__24_3_159_0,
     author = {Fefferman, Charles},
     title = {Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$},
     journal = {Annales de l'Institut Fourier},
     pages = {159--164},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {3},
     year = {1974},
     doi = {10.5802/aif.523},
     mrnumber = {52 #11574},
     zbl = {0292.26013},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.523/}
}
TY  - JOUR
AU  - Fefferman, Charles
TI  - Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$
JO  - Annales de l'Institut Fourier
PY  - 1974
SP  - 159
EP  - 164
VL  - 24
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.523/
DO  - 10.5802/aif.523
LA  - en
ID  - AIF_1974__24_3_159_0
ER  - 
%0 Journal Article
%A Fefferman, Charles
%T Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$
%J Annales de l'Institut Fourier
%D 1974
%P 159-164
%V 24
%N 3
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.523/
%R 10.5802/aif.523
%G en
%F AIF_1974__24_3_159_0
Fefferman, Charles. Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$. Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 159-164. doi : 10.5802/aif.523. http://www.numdam.org/articles/10.5802/aif.523/

[1] L.D. Kudrjavcev, Svoǐctba graničnyh značeniǐ funkciǐ iz vesovyh prostranctv i ih priloženija k kraevym zadačam. Mehanika Splošnoǐ sredy i rodstvennye problemy analiza. Moskva 1972.

[2] S.V. Uspenskiǐ, O teoremah vloženija dlja vesovyh klassov, Trudi Mat. Instta AN SSSR, 60 (1961), 282-303.

[3] V. Portnov, Doklady AN SSSR, to appear.

Cité par Sources :