L p −BOUNDS FOR THE RIESZ TRANSFORMS ASSOCIATED WITH THE HODGE LAPLACIAN IN LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS
Abstract
We prove L p-bounds for the Riesz transforms d/ √ −∆, δ/ √ −∆ associated with the Hodge-Laplacian ∆ = −δd − dδ equipped with absolute and relative boundary conditions in a Lipschitz subdomain Ω of (smooth) Riemannian manifold M, for p in a certain interval depending on the Lipschitz character of the domain.
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