L p −BOUNDS FOR THE RIESZ TRANSFORMS ASSOCIATED WITH THE HODGE LAPLACIAN IN LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS

Steve Hofmann (1) , Marius Mitrea (1) , Sylvie Monniaux (2)

1 Mizzou - University of Missouri [Columbia]
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Domaines: Equations aux dérivées partielles [math.AP]

Steve Hofmann, Marius Mitrea, Sylvie Monniaux. L p −BOUNDS FOR THE RIESZ TRANSFORMS ASSOCIATED WITH THE HODGE LAPLACIAN IN LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS. Annales de l'Institut Fourier, 2011, 61 (4), pp.1323-1349. ⟨hal-01285349⟩