$L^{p}$ estimates for multilinear maximal Bochner--Riesz means and square function

TL;DR

This paper establishes $L^{p}$ bounds for multilinear maximal Bochner--Riesz means and related square functions, extending previous bilinear results to multilinear settings using advanced harmonic analysis techniques.

Contribution

It introduces new $L^{p}$ estimates for multilinear Bochner--Riesz means, generalizing prior bilinear results to a multilinear framework.

Findings

Proved $L^{p}$ boundedness for multilinear maximal Bochner--Riesz means

Extended bilinear estimates to multilinear context

Utilized advanced harmonic analysis techniques for proofs

Abstract

In this article we have investigated $L^{p}$ boundedness of the multilinear maximal Bochner--Riesz means and the corresponding square function. We have exploited the ideas given in the paper "Maximal estimates for bilinear Bochner--Riesz means" (Adv. Math. 395(2022) 108100) by Jotsaroop and Shrivastava, in order to prove our results.