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

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

limx1→∞f(x1,x2,...,xn)=const.,a.e.inRn-1.

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

limx1→∞f(x1,x2,...,xn)=const.,p.p.dansRn-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 = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {24},
     number = {3},
     year = {1974},
     doi = {10.5802/aif.523},
     zbl = {0292.26013},
     mrnumber = {52 #11574},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.523/}
}
TY  - JOUR
TI  - Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$
JO  - Annales de l'Institut Fourier
PY  - 1974
DA  - 1974///
SP  - 159
EP  - 164
VL  - 24
IS  - 3
PB  - Imprimerie Louis-Jean
PP  - Gap
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.523/
UR  - https://zbmath.org/?q=an%3A0292.26013
UR  - https://www.ams.org/mathscinet-getitem?mr=52 #11574
UR  - https://doi.org/10.5802/aif.523
DO  - 10.5802/aif.523
LA  - en
ID  - AIF_1974__24_3_159_0
ER  - 
%0 Journal Article
%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 Imprimerie Louis-Jean
%C Gap
%U https://doi.org/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, Volume 24 (1974) no. 3, pp. 159-164. doi : 10.5802/aif.523. https://aif.centre-mersenne.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.

Cited by Sources: