Growth norm estimates for $\bar\partial$ on convex domains
Commun. Korean Math. Soc. 2007 Vol. 22, No. 1, 111-119
Printed March 1, 2007
Hong Rae Cho, Ern Gun Kwon
Pusan National University, Andong National University
Abstract : We consider the growth norm of a measurable function $f$ defined by $$ \|f\|_{-\sigma}=\text{ess\ sup}\{\delta_D(z)^\sigma|f(z)|:z\in D\}, $$ where $\delta_D(z)$ denote the distance from $z$ to $\partial D$. We prove some kind of optimal growth norm estimates for $\bar\partial$ on convex domains.
Keywords : growth norm estimates for $\bar\partial$, Lipschitz space, convex domains
MSC numbers : 32W05,32A26, 32A36
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