$L^p\to L^q$ estimates for Stein's spherical maximal operators

Naijia Liu, Minxing Shen, Liang Song +1

In this article we consider a modification of the Stein's spherical maximal operator of complex order $\alpha$ on ${\mathbb{R}}^n$: $$ {\mathfrak M}^α_{[1,2]} f(x) =\sup\limits_{t\in [1,…