Embedding weighted Hardy spaces into Lebesgue spaces and generalized area operators. Issue 4 (3rd April 2023)

• Record Type: Journal Article
• Authors: Shen, Conghui; Lou, Zengjian; Li, Songxiao
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 4(2023)
• Page Start: 603
• Page End: 618
• Publication Date: 2023-04-03
• Subjects: Weighted Hardy space -- Carleson measure -- generalized area operator; 47B38 -- 30H10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.2007379
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this paper, we consider the weighted Hardy space H p ( ω ) induced by an A p weight ω . We characterize the positive Borel measures μ such that the identity operator I d : H p ( ω ) → L q ( d μ ) is bounded when 1 ≤ p, q < ∞ . As an application, we obtain necessary and sufficient conditions for the boundedness of the generalized area operator A μ, ν from H p ( ω ) to L q ( ω ) .