Let $\mathscr{X}$ be a space of homogeneous type. Assume that $L$ has a bounded holomorphic functional calculus on $L^2(\Omega)$ and $L$ generates a semigroup with suitable upper bounds on its heat kernels where $\Omega$ is a measurable subset of $\mathscr{X}$ . For appropriate bounded holomorphic functions $b$ , we can define the operators $b(L)$ on $L^p({\Omega})$ , $1\leq p\leq \infty$ . We establish conditions on positive weight functions $u, v$ such that for each $p$ , $1
Publié le : 2005-10-14
Classification:
holomorphic functional calculus,
space of homogeneous type,
singular integral operator,
weights,
semigroup kernel,
elliptic operator,
42B25,
42B20,
47B38
@article{1150287306,
author = {DUONG, Xuan Thinh and YAN, Lixin},
title = {Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 1129-1152},
language = {en},
url = {http://dml.mathdoc.fr/item/1150287306}
}
DUONG, Xuan Thinh; YAN, Lixin. Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 1129-1152. http://gdmltest.u-ga.fr/item/1150287306/