Abstract
AbstractCoifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$\mathcal {H}^1({\mathbb {R}}^n)$$
H
1
(
R
n
)
. We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.
Funder
University of Helsinki including Helsinki University Central Hospital
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
Reference57 articles.
1. Astala, K., Iwaniec, T., Martin, G.: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane. Princeton University Press, Princeton (2009)
2. Auscher, P., Russ, E., Tchamitchian, P.: Hardy Sobolev spaces on strongly Lipschitz domains of $${\mathbb{R} }^n$$. J. Funct. Anal. 218(1), 54–109 (2005)
3. Bonami, A., Feuto, J., Grellier, S.: Endpoint for the DIV-CURL lemma in Hardy spaces. Pub. Mat. 54(2), 341–358 (2010)
4. Chen, J., Hu, G.: Compact commutators of rough singular integral operators. Canad. Math. Bull. 58(1), 19–29 (2015)
5. Clop, A., Cruz, V.: Weighted estimates for Beltrami equations. Ann. Acad. Sci. Fenn. Math. 38(1), 91–113 (2013)