XII: 26, 378-397, LNM 649 (1978)
BROSSARD, Jean
Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace. Démonstration probabiliste d'un théorème de Calderon et Stein (
Potential theory,
Real analysis)
Given a harmonic function $u$ in a half space, Stein (
Acta Math. 106, 1961) shows that the boundary points $x$ such that 1) $u$ has a non-tangential limit at $x$, 2) $u$ is ``non tangentially bounded'' near $x$, 3) $\nabla u$ is locally $L^2$ in the non-tangential cones at $x$, are the sames, except for sets of measure $0$. This result is given here a probabilistic proof using conditional Brownian motion
Keywords: Harmonic functions in a half-space,
Non-tangential limitsNature: Original
Retrieve article from Numdam
XXI: 09, 173-175, LNM 1247 (1987)
ÉMERY, Michel;
YUKICH, Joseph E.
A simple proof of the logarithmic Sobolev inequality on the circle (
Real analysis)
The same kind of semi-group argument as in Bakry-Émery
1912 gives an elementary proof of the logarithmic Sobolev inequality on the circle
Keywords: Logarithmic Sobolev inequalitiesNature: New proof of known results Retrieve article from Numdam
