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...

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Vydáno v:The Journal of Analysis Ročník 32; číslo 6; s. 3297 - 3305
Hlavní autor: Perera, Menuja
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Nature Singapore 01.12.2024
Springer Nature B.V
Témata:
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
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31
32
ISSN:0971-3611, 2367-2501
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Popis
Shrnutí: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 .
Bibliografie:ObjectType-Article-1
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ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-024-00794-5