# Low-dimensional maximal restriction principles for the Fourier transform

## TL;DR

This paper develops abstract maximal restriction principles for the Fourier transform, focusing on convolution-type maximal operators and $r$-average maximal functions, leading to new restriction estimates including spherical cases.

## Contribution

It introduces novel abstract maximal restriction results for the Fourier transform, addressing open problems for spherical and $r$-average maximal functions.

## Key findings

- Established maximal restriction estimates for convolution-type operators
- Derived spherical maximal restriction estimates
- Provided restriction estimates for 2-average maximal functions

## Abstract

Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of convolution-type and $r-$average maximal functions. As a by-product of our techniques we obtain spherical maximal restriction estimates, as well as restriction estimates for $2-$average maximal functions, answering thus points left open by V. Kova\v{c} and M\"uller, Ricci and Wright.