Multilinear Littlewood-Paley estimates with applications to partial differential equations

Eugene B Fabes; David S Jerison; Carlos E Kenig

doi:10.1073/pnas.79.18.5746

. 1982 Sep;79(18):5746–5750. doi: 10.1073/pnas.79.18.5746

Multilinear Littlewood-Paley estimates with applications to partial differential equations

Eugene B Fabes ^*, David S Jerison ^†, Carlos E Kenig ^*

PMCID: PMC346983 PMID: 16593230

Abstract

We obtain a collection of multilinear Littlewood-Paley estimates, which we then apply to two problems in partial differential equations. The first problem is the estimation of the square root of an elliptic operator in divergence form, and the second is the estimation of solutions to the Cauchy problem for nondivergence-form parabolic equations.

Keywords: elliptic operators, Kato's problem, parabolic Cauchy problem, square Dini condition