Further regularity results in P-extremal setting

In our paper, Pluripotential theory and convex bodies: a Siciak-Zaharjuta theorem (Computational Methods and Function Theory (2020), 20(3-4), 571-590) by Bayraktar et al., we proved a regularity result of P - extremal function. In this paper, we prove some other stronger regularity results analogue...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of Analysis Vol. 32; no. 6; pp. 3297 - 3305
Main Author: Perera, Menuja
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.12.2024
Springer Nature B.V
Subjects:
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Measure and Integration
Original Research Paper
Special Functions
Pluripotential theory
Convex body
Extremal functions
Regularity
30
31
32
ISSN:0971-3611, 2367-2501
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In our paper, Pluripotential theory and convex bodies: a Siciak-Zaharjuta theorem (Computational Methods and Function Theory (2020), 20(3-4), 571-590) by Bayraktar et al., we proved a regularity result of P - extremal function. In this paper, we prove some other stronger regularity results analogue to those in the standard setting. Specifically we focus on proving the following proposition: Proposition: Let K = D ¯ ⊂ C d be the closure of a bounded domain D with ∂ D of class C 1 , 1 . Then, for any Q ∈ C α ( K ) , where C α ( K ) is the Hölder class α on K , we have V P , K , Q ∈ C α ( C d ) for a convex body P ⊂ ( R + ) d .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-024-00794-5