Sobolev spaces on bounded symmetric domains

Abstract

We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains.

Keywords:

• bounded symmetric domain
• Sobolev space
• Bergman space

AMS Subject Classifications:

• Primary: 32M15
• Secondary: 32A36
• 46E35

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

Research supported by GA ČR [grant number 201/12/0426] and by RVO funding for IČ [67985840].