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Collectanea Mathematica

, Volume 69, Issue 3, pp 427–435 | Cite as

Sparse endpoint estimates for Bochner–Riesz multipliers on the plane

  • Robert Kesler
  • Michael T. Lacey
Article
  • 51 Downloads

Abstract

For \( 0< \lambda < \frac{1}{2}\), let \( B _{\lambda }\) be the Bochner–Riesz multiplier of index \( \lambda \) on the plane. Associated to this multiplier is the critical index \(1< p_ \lambda = \frac{4}{3+2 \lambda } < \frac{4}{3}\). We prove a sparse bound for \( B _{\lambda }\) with indices \( (p_ \lambda , q)\), where \( p_ \lambda '< q < 4\). This is a further quantification of the endpoint weak \(L^{p_ \lambda }\) boundedness of \( B _{\lambda }\), due to Seeger. Indeed, the sparse bound immediately implies new endpoint weighted weak type estimates for weights in \( A_1 \cap RH _{\rho }\), where \( \rho > \frac{4}{4 - 3 p _{\lambda }}\).

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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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