Multilinear estimates for Calder\'on commutators
Xudong Lai

TL;DR
This paper establishes all endpoint multilinear boundedness estimates for higher-order Calderón commutators in higher dimensions, generalizing known one-dimensional results and exploring limitations for certain target spaces.
Contribution
It provides the first comprehensive endpoint estimates for multilinear Calderón commutators in dimensions greater than two, including new counterexamples and potential applications.
Findings
Established multilinear endpoint estimates for Calderón commutators in higher dimensions.
Proved the boundedness of the commutator from specific Lorentz and Lebesgue spaces.
Identified limitations of these estimates for certain target space exponents.
Abstract
In this paper, we investigate the multilinear boundedness properties of the higher (-th) order Calder\'on commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space , including that Calder\'on commutator maps the product of Lorentz spaces to , which is the higher dimensional nontrivial generalization of the endpoint estimate that the -th order Calder\'on commutator maps to . When considering the target space with , some counterexamples are given to show that these multilinear estimates may not hold. The method…
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Nonlinear Partial Differential Equations
