Abstract
AbstractWe prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight p-Poincaré inequality in such domains. As an application we show that certain nonnegative supersolutions of the p-Laplace equation and distance weights are p-admissible in a bounded domain, in the sense that they support versions of the p-Poincaré inequality.
Funder
Emil Aaltosen Säätiö
Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. Björn, A., Björn, J.: Nonlinear Potential Theory on Metric Spaces, EMS Tracts in Mathematics, vol. 17. European Mathematical Society (EMS), Zürich (2011)
2. Boman, J.: $$L^p$$-Estimates for Very Strongly Elliptic Systems, Technical Report 29. Department of Mathematics, Stockholm University (1982)
3. Buckley, S.M., Koskela, P., Lu, G.: Boman Equals John, XVIth Rolf Nevanlinna Colloquium (Joensuu, 1995), pp. 91–99 (1996)
4. Chanillo, S., Wheeden, R.L.: Poincaré inequalities for a class of non-$$A_p$$ weights. Indiana Univ. Math. J. 41(3), 605–623 (1992)
5. Chua, S.-K.: Weighted Sobolev inequalities on domains satisfying the chain condition. Proc. Am. Math. Soc. 117(2), 449–457 (1993)