A Note on Endpoint Bochner-Riesz Estimates

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Date

Volume

17

Issue

Journal

Series Titel

Oberwolfach Preprints (OWP)

Book Title

Publisher

Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach

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Abstract

We revisit an $\varepsilon$-removal argument of Tao to obtain sharp $L^p \to L^r(L^p)$ estimates for sums of Bochner-Riesz bumps which are conditional on non-endpoint bounds for single scale bumps. These can be used to obtain sharp conditional sparse bounds for Bochner-Riesz multipliers at the critical index, refining the conditional weak-type $(p,p)$ estimates of Tao.

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Keywords

Bochner-Riesz Means, Weak-Type Estimates

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