A note for Carleson measure on bounded C-convex domains

Key Points

• To establish characterizations for boundedness of Carleson embedding on bounded C-convex domains and its equivalence to compactness.
• Analyzed Carleson measure in the context of bounded C-convex domains.
• Established equivalences related to the boundedness of the Carleson embedding.
• Focused on the embedding from A_α^p to L^q(μ) on the domain Ω.
• Identified multiple characterizations for boundedness of Carleson embedding.
• Demonstrated that boundedness is equivalent to compactness under the sharp B condition.