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On pointwise convergence of cone multipliers

Published 4 May 2024 in math.CA | (2405.02607v1)

Abstract: For $p\ge 2$, and $\lambda>\max{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t\lambda(f)\to f \text{ a.e.},$$ where $f\in Lp(\mathbb Rn)$ satisfies $supp\ \widehat f\subset{\xi\in\mathbb Rn:\ 1<|\xi_n|<2}$. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.

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