On the boundary limits of harmonic functions with gradient in $L^p$

Mizuta, Yoshihiro. "On the boundary limits of harmonic functions with gradient in $L^p$." Annales de l'institut Fourier 34.1 (1984): 99-109. <http://eudml.org/doc/74623>.

@article{Mizuta1984,
abstract = {This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in $L^n(\{\bf R\}^n_+)$, $\{\bf R\}^n_+$ denoting the upper half space of the $n$-dimensional euclidean space $\{\bf R\}^n$. Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation of precise functions given by Ohtsuka (Lecture Notes, Hiroshima Univ., 1973).},
author = {Mizuta, Yoshihiro},
journal = {Annales de l'institut Fourier},
keywords = {tangential boundary behaviors; harmonic functions with gradient in Lebesgue classes; integral representation},
language = {eng},
number = {1},
pages = {99-109},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the boundary limits of harmonic functions with gradient in $L^p$},
url = {http://eudml.org/doc/74623},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Mizuta, Yoshihiro
TI - On the boundary limits of harmonic functions with gradient in $L^p$
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 1
SP - 99
EP - 109
AB - This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in $L^n({\bf R}^n_+)$, ${\bf R}^n_+$ denoting the upper half space of the $n$-dimensional euclidean space ${\bf R}^n$. Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation of precise functions given by Ohtsuka (Lecture Notes, Hiroshima Univ., 1973).
LA - eng
KW - tangential boundary behaviors; harmonic functions with gradient in Lebesgue classes; integral representation
UR - http://eudml.org/doc/74623
ER -