Restriction of Hardy space to linear subvarieties

Abstract

We consider an operator which restricts a holomorphic function to a linear subvariety. We prove that if for any complex linear affine subvariety the restriction operator maps the Hardy space onto the Bergman space on a subvariety then the boundary is at each point of multitype . This is applied as a test to complex ellipsoids.

Keywords:

• interpolation
• restriction
• Hardy space
• Bergman space
• multitype

AMS Subject Classifications:

• 32A35
• 32A36
• 32F32
• 32T25
• 32T27