Multilinear analysis on metric spaces
Volume 497 / 2014
Dissertationes Mathematicae 497 (2014), 1-121
MSC: Primary 42B20, 42B25, 42B35; Secondary 35S50,
42C15, 47G30, 30L99.
DOI: 10.4064/dm497-0-1
Abstract
The multilinear Calderón–Zygmund theory is developed in the setting of $\mathrm{RD}$-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.
