Weighted $L^p$ Estimates of Kato Square Roots Associated to Degenerate Elliptic Operators

Publication date: 17 September 2015

Abstract: Let

w

be a Muckenhoupt

A_{2} (m a t h b b R^{n})

weight and

L_{w} : = - w^{- 1} m a t h o p m a t h r m d i v (A a b l a)

the degenerate elliptic operator on the Euclidean space

m a t h b b R^{n}

,

n g e q 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 i n A_{p} (m a t h b b R^{n})

,

p i n (f r a c 2 n n + 1,, 2]

and any

f i n C^{i} n f t y_{c} (m a t h b b R^{n})

,

| L_{w}^{1 / 2} (f) |_{L^{p} (w,, m a t h b b R^{n})} s i m | a b l a f |_{L^{p} (w,, m a t h b b R^{n})}

, where

C_{c}^{i} n f t y (m a t h b b R^{n})

denotes the set of all infinitely differential functions with compact supports.

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