Embedding weighted Hardy spaces into Lebesgue spaces and generalized area operators.

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). [ABSTRACT FROM AUTHOR]