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Poisson semigroups and singular integrals


Author: Björn E. J. Dahlberg
Journal: Proc. Amer. Math. Soc. 97 (1986), 41-48
MSC: Primary 42B25; Secondary 31B20, 42B20
DOI: https://doi.org/10.1090/S0002-9939-1986-0831384-0
MathSciNet review: 831384
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Abstract: Let $ D \subset {{\mathbf{R}}^n}$ be a Lipschitz domain and consider the bilinear form $ \int_D {u\left( {\partial v/\partial y} \right)dP} $. We show that the form is bounded if $ v$ is harmonic with boundary values in $ {L^2}$, if $ u$ is smooth with its nontangential maximal function in $ {L^2}$ and $ \int_D {{\text{dist}}\left\{ {P,\partial D} \right\}{{\left\vert {{\text{grad }}u} \right\vert}^2}dP < \infty } $.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0831384-0
Article copyright: © Copyright 1986 American Mathematical Society

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