Sparse endpoint estimates for Bochner–Riesz multipliers on the plane

• Autores: Robert Kesler, Michael T. Lacey
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 3, 2018, págs. 427-435
• Idioma: inglés
• DOI: 10.1007/s13348-018-0214-1
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• Resumen

  • 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 }}.