The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces, and Triebel-Lizorkin spaces are also proved. Applications include the boundedness of paraproducts and bilinear multiplier operators on products of Besov and Triebel-Lizorkin spaces.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm497-0-1,
author = {Loukas Grafakos and Liguang Liu and Diego Maldonado and Dachun Yang},
title = {Multilinear analysis on metric spaces},
series = {GDML\_Books},
year = {2014},
zbl = {1301.42025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm497-0-1}
}
Loukas Grafakos; Liguang Liu; Diego Maldonado; Dachun Yang. Multilinear analysis on metric spaces. GDML_Books (2014), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm497-0-1/