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arXiv · 2304.02816

Small cap square function estimates

Shengwen Gan
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Abstract

We introduce small cap square function estimates for parabola and cone, and prove the sharp estimates. More precisely, we study the inequalities of form \[ \|f\|_p\le C_{\alpha,p}(R) \Big\|(\sum_{\gamma\in\Gamma_\alpha(R^{-1})}|f_\gamma|^2)^{1/2}\Big\|_p, \] where $\Gamma_\alpha(R^{-1})$ is the set of small caps of width $R^{-\alpha}$. We find the sharp constant $C_{\alpha,p}(R)$.

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Shengwen Gan. 2023-04-06. Small cap square function estimates. https://arxiv.org/abs/2304.02816

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