We give a condition under which a divisor X in a bounded convex domain of finite type D in C^n is the zero set of a function in a Hardy space H^p(D) for some p > 0. This generalizes Varopoulos' result [Zero sets of H^p functions in several complex variables, Pac. J. Math. (1980)] on zero sets of H^p-functions in strictly convex domains of C^n .
Published in Mathematische Zeitschrift
We obtain sharp weighted estimates for solutions of the equation ∂¯u=f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\partial }u=f$$\end{document} in a linea...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...
