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arXiv · 1903.10265

Strict singularity of weighted composition operators on derivative Hardy spaces

Qingze Lin·Junming Liu·Yutian Wu
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Abstract

We prove that the weighted composition operator $W_{ϕ,φ}$ fixes an isomorphic copy of $\ell^p$ if the operator $W_{ϕ,φ}$ is not compact on the derivative Hardy space $S^p$. In particular, this implies that the strict singularity of the operator $W_{ϕ,φ}$ coincides with the compactness of it on $S^p$. Moreover, when $p\neq2$, we characterize the conditions for those weighted composition operators $W_{ϕ,φ}$ on $S^p$ which fix an isomorphic copy of $\ell^2$ .

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Qingze Lin, Junming Liu, Yutian Wu. 2019-03-26. Strict singularity of weighted composition operators on derivative Hardy spaces. https://arxiv.org/abs/1903.10265

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