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arXiv · 2505.18509

Bilinear Bochner-Riesz Means for Grushin Operators

Sayan Bagchi·Md Nurul Molla·Joydwip Singh
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Abstract

This paper is devoted to the study of $L^{p_1} \times L^{p_2}$ to $L^{p}$ boundedness of the bilinear Bochner-Riesz mean $\mathcal{B}^{\alpha}$ associated with the Grushin operator $\mathcal{L} = -\Delta_{x'} - |x'|^2 \Delta_{x''}$ on $\mathbb{R}^{d_1} \times \mathbb{R}^{d_2}$. Our result almost resembles the corresponding Euclidean results, where the Euclidean dimension in the smoothness threshold is replaced by the topological dimension $d$ of the underlying space, except at few cases.

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Sayan Bagchi, Md Nurul Molla, Joydwip Singh. 2025-05-24. Bilinear Bochner-Riesz Means for Grushin Operators. https://arxiv.org/abs/2505.18509

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