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dc.contributor.authorHytönen, T.
dc.contributor.authorLi, K.
dc.contributor.authorSawyer, E.
dc.date.accessioned2021-05-13T10:56:39Z
dc.date.available2021-05-13T10:56:39Z
dc.date.issued2020
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1288
dc.description.abstractWe 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 \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 $\left\ | 2Q\right\ |_{\omega }\leq D\left\ | Q\right\ |_{\omega }$.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleRESTRICTED TESTING FOR POSITIVE OPERATORSen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.arxiv1809.04873
dc.relation.projectIDES/1PE/SEV-2017-0718en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/submittedVersionen_US


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