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arXiv · 1608.07199

A Two-weight inequality between $L^p(\ell^2)$ and $L^p$

Tuomas Hytönen·Emil Vuorinen
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Abstract

We consider boundedness of a certain positive dyadic operator $$ T^\sigma \colon L^p(\sigma; \ \! \ell^2) \to L^p(\omega), $$ that arose during our attempts to develop a two-weight theory for the Hilbert transform in $L^p$. Boundedness of $T^\sigma$ is characterized when $p \in [2, \infty)$ in terms of certain testing conditions. This requires a new Carleson-type embedding theorem that is also proved.

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Tuomas Hytönen, Emil Vuorinen. 2016-08-25. A Two-weight inequality between $L^p(\ell^2)$ and $L^p$. https://doi.org/10.1112/s0025579317000511

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