On the Good-$\lambda$ inequality for nonlinear potentials
Abstract
This note concerns an extension of the good- 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- 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.
Cite
@article{arxiv.1105.6152,
title = {On the Good-$\lambda$ inequality for nonlinear potentials},
author = {Petr Honzík and Benjamin J. Jaye},
journal= {arXiv preprint arXiv:1105.6152},
year = {2012}
}
Comments
13 pages, submitted