WEIGHTED Lp ESTIMATES OF KATO SQUARE ROOTS ASSOCIATED TO DEGENERATE ELLIPTIC

Let w be a Muckenhoupt A(2) (R-n) weight and L-w := -w(-1) div (A del) the degenerate elliptic operator on the Euclidean space R-n, n >= 2. In this article, the authors establish some weighted L-p estimates of Kato square roots associated to the degenerate elliptic operators L-w. More precisely, the authors prove that, for w is an element of A(p) (R-n), p is an element of (2n/n+1, 2] and any f is an element of C-c(infinity) (R-n), parallel to L-w(1/2) (f)parallel to(Lp (w,Rn)) similar to parallel to del f parallel to(Lp (w,Rn)), where C-c(infinity) (R-n) denotes the set of all infinitely differential functions with compact supports and the implicit equivalent positive constants are independent of f.