Embedding weighted Hardy spaces into Lebesgue spaces and generalized area operators. Issue 4 (3rd April 2023) - Shen, Conghui; Lou, Zengjian; Li, Songxiao
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 ) .