Dirichlet integral and star-function inequalities
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- by J. R. Quine PDF
- Proc. Amer. Math. Soc. 96 (1986), 249-254 Request permission
Abstract:
Let $\lambda (z)$ be a smooth function in an annulus, $\tilde \lambda (z)$ its symmetric rearrangement and ${\lambda ^ * }(z)$ its star-function. A formula is proved relating $\Delta {\lambda ^ * },\Delta \lambda$, and the Dirichlet integrands of $\lambda$ and $\tilde \lambda$. The formula shows the relationship between Dirichlet integral inequalities and the subharmonicity of ${\lambda ^ * }$ for subharmonic $\lambda$, and gives an explicit formula for $\Delta {\lambda ^ * }$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 249-254
- MSC: Primary 31A05; Secondary 30C55, 30D35
- DOI: https://doi.org/10.1090/S0002-9939-1986-0818454-8
- MathSciNet review: 818454