On the good-λ inequality for nonlinear potentials

0386972 - MÚ 2013 RIV US eng J - Journal Article
Honzík, Petr - Jaye, B.J.
On the good-λ inequality for nonlinear potentials.
Proceedings of the American Mathematical Society. Roč. 140, č. 12 (2012), s. 4167-4180. ISSN 0002-9939. E-ISSN 1088-6826
R&D Projects: GA AV ČR KJB100190901
Institutional research plan: CEZ:AV0Z10190503
Keywords : weighted norm inequalities * good-A inequality * elliptic equations
Subject RIV: BA - General Mathematics
Impact factor: 0.609, year: 2012
http://www.ams.org/journals/proc/2012-140-12/S0002-9939-2012-11352-8/home.html

This paper concerns an extension of the good-A inequality for fractional integrals, due to B. Muckenhoupt and R. Wheeden. The classical result is refined in two aspects. Firstly, general nonlinear potentials are considered, and secondly, the constant in the inequality is proven to decay exponentially. As a consequence, the exponential integrability of the gradient of solutions to certain quasilinear elliptic equations is deduced. This in turn is a consequence of certain Morrey space embeddings which extend classical results for the Riesz potential. In addition, the good-A inequality proved here provides an elementary proof of the result of Jawerth, Perez and Welland regarding the positive cone in certain weighted Triebel-Lizorkin spaces.
Permanent Link: http://hdl.handle.net/11104/0219991