dc.contributor.author Hytönen, T. dc.contributor.author Li, K. dc.contributor.author Sawyer, E. dc.date.accessioned 2021-05-13T10:56:39Z dc.date.available 2021-05-13T10:56:39Z dc.date.issued 2020 dc.identifier.uri http://hdl.handle.net/20.500.11824/1288 dc.description.abstract We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality en_US \begin{equation*} \int_{\mathbb{R}^{n}}T\left( f\sigma \right) ^{2}d\omega \leq C\int_{\mathbb{ R}^{n}}f^{2}d\sigma \end{equation*} holds for all $f\geq 0$ if and only if the (fractional) $A_2$ condition holds, and the restricted testing condition $\int_{Q}T\left( 1_{Q}\sigma \right) ^{2}d\omega \leq C\left\ | Q\right\ |_{\sigma }$ holds for all cubes $Q$ satisfying $\left\ | 2Q\right\ |_{\sigma }\leq D\left\ | Q\right\ |_{\sigma }$. If T is linear, we require as well that the dual restricted testing condition $\begin{equation*} \int_{Q}T^{\ast }\left( 1_{Q}\omega \right) ^{2}d\sigma \leq C\left\ | Q\right\ |_{\omega } \end{equation*} holds for all cubes Q satisfying$\left\ | 2Q\right\ |_{\omega }\leq D\left\ | Q\right\ |_{\omega }\$. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title RESTRICTED TESTING FOR POSITIVE OPERATORS en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.arxiv 1809.04873 dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/submittedVersion en_US
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