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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 $\mathcal{H}^p(\omega)$ induced by an $A_1$ weight $\omega.$ We characterize the positive Borel measure $\mu$ such that the identical operator maps $\mathcal{H}^p(\omega)$ into $L^q(d\mu)$ boundedly when $0<p, q<\infty.$ As an application, we obtain necessary and sufficient conditions for the boundedness of generalized area operators $A_{\mu,\nu}$ from $\mathcal{H}^p(\omega)$ to $L^q(\omega).$

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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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