Poisson semigroups and singular integrals
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- by Björn E. J. Dahlberg PDF
- Proc. Amer. Math. Soc. 97 (1986), 41-48 Request permission
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 $\int _D {{\text {dist}}\left \{ {P,\partial D} \right \}{{\left | {{\text {grad }}u} \right |}^2}dP < \infty }$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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