Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators are studied. We prove that -uniform, 1 < p < ∞, spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on p. We also characterize L¹-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-1-4,
author = {B\l a\.zej Wr\'obel},
title = {Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {47-67},
zbl = {1286.42012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-1-4}
}
Błażej Wróbel. Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators. Studia Mathematica, Tome 215 (2013) pp. 47-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-1-4/