Weighted endpoint bounds for the Bergman and Cauchy-Szeg\H{o} projections on domains with near minimal smoothness

Autor:	Stockdale, Cody B., Wagner, Nathan A.
Rok vydání:	2020
Předmět:	Mathematics - Complex Variables Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis 32A50 32A25 32A26 32A35 32A36 42B20
Zdroj:	Indiana Univ. Math. J. 71 (2022), no. 5, 2099-2125
Druh dokumentu:	Working Paper
Popis:	We study the Bergman projection, $\mathcal{B}$, and the Cauchy-Szeg\H{o} projection, $\mathcal{S}$, on bounded domains with near minimal smoothness. We prove that $\mathcal{B}$ has the weak-type $(1,1)$ property with respect to weighted measures assuming that the underlying domain is strongly pseudoconvex with $C^4$ boundary and the weight satisfies the $B_1$ condition, and the same property for $\mathcal{S}$ on domains with $C^3$ boundaries and weights satisfying the $A_1$ condition. We also obtain weighted Kolmogorov and weighted Zygmund inequalities for $\mathcal{B}$ and $\mathcal{S}$ in their respective settings as corollaries. Comment: 22 pages. To appear in Indiana University Mathematics Journal
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.12261 Zobrazit plný text záznamu View this record from Arxiv