L Bounds for Riesz Transforms and Square Roots Associated to Second Order Elliptic Operators
نویسنده
چکیده
We consider the Riesz transforms ∇L−1/2, where L ≡ −divA(x)∇, and A is an accretive, n× n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the square root problem of T. Kato.
منابع مشابه
Bounds of Riesz Transforms on L Spaces for Second Order Elliptic Operators
Let L = −div(A(x)∇) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on Rn or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2, a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ∇(L)−1/2 on the Lp space. As an application, for 1 < p < 3+ ε, we establish the Lp boundedness...
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