CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Growth Spaces and Growth Norm Estimates for $\Bar\partial$ on Convex Domains of Finite Type

  Published:2006-12-01
 Printed: Dec 2006
  • Hong Rae Cho
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We consider the growth norm of a measurable function $f$ defined by $$\|f\|_{-\sigma}=\ess\{\delta_D(z)^\sigma|f(z)|:z\in D\},$$ where $\delta_D(z)$ denote the distance from $z$ to $\partial D$. We prove some optimal growth norm estimates for $\bar\partial$ on convex domains of finite type.
MSC Classifications: 32W05, 32A26, 32A36 show english descriptions $\overline\partial$ and $\overline\partial$-Neumann operators
Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)
Bergman spaces
32W05 - $\overline\partial$ and $\overline\partial$-Neumann operators
32A26 - Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)
32A36 - Bergman spaces
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/