Growth Spaces and Growth Norm Estimates for on Convex Domains of Finite Type

Cho, Hong Rae

Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 508-525

Résumé

We consider the growth norm of a measurable function $f$ defined by $${{\left\| f \right\|}_{-\sigma }}=\text{ess}\,\,\text{sup}\left\{ {{\delta }_{D}}{{\left( z \right)}^{\sigma }}\left| f\left( z \right) \right|:z\in D \right\},$$ where ${{\delta }_{D}}\left( z \right)$ denote the distance from $z$ to $\partial D$ . We prove some optimal growth norm estimates for $\bar{\partial }$ on convex domains of finite type.

Détail

DOI : 10.4153/CMB-2006-049-3

Mots-clés : 32W05, 32A26, 32A36

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