We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.
@article{urn:eudml:doc:41381, title = {An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.}, journal = {Publicacions Matem\`atiques}, volume = {43}, year = {1999}, pages = {685-711}, mrnumber = {MR1744625}, zbl = {0959.35027}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41381} }
Auscher, Pascal; Tchamitchian, Philippe. An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.. Publicacions Matemàtiques, Tome 43 (1999) pp. 685-711. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41381/