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Lp-boundedness (1 ≤ p ≤ ∞) for Bergman Projection on a Class of Convex Domains of Infinite Type in C2

Ly Kim Ha
경북대학교 자연과학대학 수학과|2023.09|Kyungpook Mathematical Journal|제63권 제3호|pp. 413-424|DOI 10.5666/KMJ.2023.63.3.413

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키워드

Bloch functionsBergman projectionfinite/infinite typeBesov functions
주제분류수학

초록

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ C2, for 1 < p < ∞, the Bergman projection P is bounded from Lp(Ω, dV ) to the Bergman space Ap(Ω); from L∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L1(Ω, P(z, z)dV ) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

Abstract

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ C2, for 1 < p < ∞, the Bergman projection P is bounded from Lp(Ω, dV ) to the Bergman space Ap(Ω); from L∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L1(Ω, P(z, z)dV ) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

참고문헌 (20)

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관련 논문AI추천

A Note on Lipschitz Estimates for Weighted Bergman Projections on Convex Domains of Infinite Type in C^2Ly Kim Ha경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2025 · 제65권 제2호Bergman type operators on some generalized Cartan-Hartogs domainsLe He, Yanyan Tang, Zhenhan Tu대한수학회 · 대한수학회지2021 · 제58권 제6호Lp SOBOLEV MAPPING PROPERTIES OF THE BERGMAN PROJECTIONS ON n-DIMENSIONAL GENERALIZED HARTOGS TRIANGLESShuo Zhang대한수학회 · 대한수학회보2021 · 제58권 제6호Lp-BOUNDEDNESS OF THE CAUCHY-LERAY-FANTAPPIÈ INTEGRAL ON CERTAIN CLASS OF WEAKLY PSEUDOCONVEX DOMAINS IN C2Ly Kim Ha, Pham Huu Trung대한수학회 · 대한수학회보2024 · 제61권 제6호On H\"older estimates for Cauchy transforms on convex domains in $\mathbb{C}^2$Ly Kim Ha대한수학회 · 대한수학회보2019 · 제56권 제4호On the Bergman kernel for some Hartogs domains박종도대한수학회 · 대한수학회보2020 · 제57권 제2호

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