Convergence on almost every line for functions with gradient in $L^p\left({𝐑}^n\right)$

Fefferman, Charles. "Convergence on almost every line for functions with gradient in $L^p({\bf R}^n)$." Annales de l'institut Fourier 24.3 (1974): 159-164. <http://eudml.org/doc/74181>.

@article{Fefferman1974,
abstract = {We prove that if $\{\rm grad\}\,(f)\in L^p(R^n)$ for certain values of $p$, then\begin\{\}\lim \_\{x\_1\rightarrow \infty \}f(x\_1,x\_2,\ldots ,x\_n)=~\text\{const.,\} \text\{a.e.\} \text\{in\}~ R^\{n-1\}.\end\{\}},
author = {Fefferman, Charles},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {159-164},
publisher = {Association des Annales de l'Institut Fourier},
title = {Convergence on almost every line for functions with gradient in $L^p(\{\bf R\}^n)$},
url = {http://eudml.org/doc/74181},
volume = {24},
year = {1974},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 3
SP - 159
EP - 164
AB - We prove that if ${\rm grad}\,(f)\in L^p(R^n)$ for certain values of $p$, then\begin{}\lim _{x_1\rightarrow \infty }f(x_1,x_2,\ldots ,x_n)=~\text{const.,} \text{a.e.} \text{in}~ R^{n-1}.\end{}
LA - eng
UR - http://eudml.org/doc/74181
ER -