On families between the Hardy–Littlewood and spherical maximal functions
Volume 59, Issue 2 (2021), pp. 323–343
Pub. online: 11 November 2021
Type: Article
Open Access
Open Access
Received
5 May 2020
5 May 2020
Revised
16 November 2020
16 November 2020
Accepted
27 November 2020
27 November 2020
Published
11 November 2021
11 November 2021
Abstract
We study a family of maximal operators that provides a continuous link connecting the Hardy–Littlewood maximal function to the spherical maximal function. Our theorems are proved in the multilinear setting but may contain new results even in the linear case. For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.