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We study two dierent local H p spaces, 0 <p 1, on a smooth domain in R n , by means of maximal functions and atomic decomposition. We prove the regularity in these spaces, as well as in the corresponding dual BMO spaces, of the Dirichlet and Neumann problems for the Laplacian.

Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in 𝐑^{𝐍}