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Regularity estimates for Green operators of Dirichlet and Neumann problems on weighted Hardy spaces
2018
In this paper we first study the generalized weighted Hardy spaces $H^p_{L,w}(X)$ for $0self-adjoint operators $L$ satisfying Gaussian upper bounds on the space of homogeneous type $X$ in both cases of finite and infinite measure. We show that the weighted Hardy spaces defined via maximal functions and atomic decompositions coincide. Then we prove weighted regularity estimates for the Green operators of the inhomogeneous Dirichlet and Neumann problems in suitable bounded or unbounded domains including bounded semiconvex domains, convex regions above a Lipschitz graph and upper half-spaces. Our estimates are in terms of weighted $L^p$ spaces for the range $1Hardy spaces for the range $0Hardy spaces for the full range $0
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