Weak $L_{1}$ characterizations of Poisson integrals, Green potentials and $H^{p}$ spaces
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- by Peter Sjögren PDF
- Trans. Amer. Math. Soc. 233 (1977), 179-196 Request permission
Abstract:
Our main result can be described as follows. A subharmonic function u in a suitable domain $\Omega$ in ${{\mathbf {R}}^n}$ is the difference of a Poisson integral and a Green potential if and only if u divided by the distance to $\partial \Omega$ is in weak ${L_1}$ in $\Omega$. Similar conditions are given for a harmonic function to be the Poisson integral of an ${L_p}$ function on $\partial \Omega$. Iterated Poisson integrals in a polydisc are also considered. As corollaries, we get weak ${L_1}$ characterizations of ${H^p}$ spaces of different kinds.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 233 (1977), 179-196
- MSC: Primary 31B10
- DOI: https://doi.org/10.1090/S0002-9947-1977-0463462-1
- MathSciNet review: 0463462