Alexandre, William

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 .

Charpentier, P. Dupain, Y.
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...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...

Hamann, Kaylee Joy

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 ...