$\ell^p$-improving inequalities for Discrete Spherical Averages

23 Jul 2019 Kesler Robert Lacey Michael T.

Let $ \lambda ^2 \in \mathbb N $, and in dimensions $ d\geq 5$, let $ A_{\lambda } f (x)$ denote the average of $ f \;:\; \mathbb Z ^{d} \to \mathbb R $ over the lattice points on the sphere of radius $\lambda$ centered at $x$. We prove $ \ell ^{p}$ improving properties of $ A_{\lambda }$... (read more)

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