Embedding Theorem For Weighted Hardy Spaces into Lebesgue Spaces

Zengjian Lou; Conghui Shen

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arXiv · 1909.03678

Embedding Theorem For Weighted Hardy Spaces into Lebesgue Spaces

Zengjian Lou·Conghui Shen

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Abstract

In this paper, we consider the weighted Hardy space $\mathcal{H}^p(ω)$ induced by an $A_1$ weight $ω.$ We characterize the positive Borel measure $μ$ such that the identical operator maps $\mathcal{H}^p(ω)$ into $L^q(dμ)$ boundedly when $0<p, q<\infty.$ As an application, we obtain necessary and sufficient conditions for the boundedness of generalized area operators $A_{μ,ν}$ from $\mathcal{H}^p(ω)$ to $L^q(ω).$

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BibTeX RIS

Zengjian Lou, Conghui Shen. 2019-09-09. Embedding Theorem For Weighted Hardy Spaces into Lebesgue Spaces. https://arxiv.org/abs/1909.03678

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