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arXiv · 2309.13487

Bochner-Riesz means at the critical index: Weighted and sparse bounds

David Beltran·Joris Roos·Andreas Seeger
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Abstract

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension $d=2$; partial results as well as conditional results are proved in higher dimensions. For the means of index $\lambda_*=\frac{d-1}{2d+2}$ we prove fully optimal sparse bounds.

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David Beltran, Joris Roos, Andreas Seeger. 2023-09-23. Bochner-Riesz means at the critical index: Weighted and sparse bounds. https://doi.org/10.1007/s00208-024-02962-1

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