Modern singular integral theory with mild kernel regularity
Classical Analysis and ODEs
2020-09-28 v3
Abstract
We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the UMD-extensions of linear Calder\'on-Zygmund operators with mild kernel regularity and extend our new proof to the multilinear setting improving recent UMD-valued estimates of multilinear singular integrals. Next, we develop the product space theory of the multilinear singular integrals with modified Dini-type assumptions, and use this theory to prove bi-parameter weighted estimates and two-weight commutator estimates.
Cite
@article{arxiv.2006.05807,
title = {Modern singular integral theory with mild kernel regularity},
author = {Emil Airta and Henri Martikainen and Emil Vuorinen},
journal= {arXiv preprint arXiv:2006.05807},
year = {2020}
}
Comments
v2: New results in UMD spaces; v3: product space theory now also multilinear, 82 pages