Corpus ID: 235727472

# Bilinear Bochner-Riesz square function and applications

@inproceedings{Choudhary2021BilinearBS,
title={Bilinear Bochner-Riesz square function and applications},
author={Surjeet Singh Choudhary and K. Jotsaroop and S. Shrivastava and K. Shuin},
year={2021}
}
In this paper we introduce Stein’s square function associated with bilinear BochnerRiesz means and develop a systematic study of its L boundedness properties. We also discuss applications of bilinear Bochner-Riesz square function in the context of bilinear fractional Schrödinger multipliers, generalized bilinear spherical maximal function and more general bilinear multipliers defined on R of the form (ξ, η) → m ( |(ξ, η)| )

#### References

SHOWING 1-10 OF 39 REFERENCES
Maximal Operators Associated with Bilinear Multipliers of Limited Decay
• Mathematics
• 2018
Results analogous to those proved by Rubio de Francia [28] are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus our attentionExpand
Boundedness of the bilinear Bochner-Riesz means in the non-Banach triangle case
• Mathematics
• 2017
In this article, we investigate the boundedness of the bilinear Bochner-Riesz means $S^{\alpha }$ in the non-Banach triangle case. We improve the corresponding results in [Bern] in two aspects: OurExpand
Weighted Estimates for Bilinear Bochner-Riesz Means at the Critical Index
• Mathematics
• 2020
In this paper we establish weighted estimates for the bilinear Bochner-Riesz operator $\mathcal B^{\alpha }$ at the critical index $\alpha =n-\frac {1}{2}$ with respect to bilinear weights.
The bilinear Bochner-Riesz problem
• Mathematics
• 2012
Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 - {\left| \xi \right|^2} - {\left| \etaExpand
Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators
• Mathematics
• 2019
We study the maximal estimates for the bilinear spherical average and the bilinear Bochner-Riesz operator. Firstly, we obtain $L^p\times L^q \to L^r$ estimates for the bilinear spherical maximalExpand
SQUARE FUNCTIONS AND MAXIMAL OPERATORS ASSOCIATED WITH RADIAL FOURIER MULTIPLIERS
• Mathematics
• 2012
We begin with an overview on square functions for spherical and Bochner– Riesz means which were introduced by Eli Stein, and discuss their implications for radial multipliers and associated maximalExpand
Square function estimates for the Bochner-Riesz means
We consider the square function (known as Stein's square function) estimate associated with the Bochner-Riesz means. The previously known range of sharp estimate is improved. Our results are based onExpand
Unboundedness of the Ball Bilinear Multiplier Operator
• Mathematics
• Nagoya Mathematical Journal
• 2007
Abstract For all n > 1, the characteristic function of the unit ball in ℝ2n is not the symbol of a bounded bilinear multiplier operator from Lp (ℝn ) × Lq (ℝn ) to Lr (ℝn ) when 1/p + 1/q = 1/r andExpand
Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators
In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.
STEIN’S SQUARE FUNCTION Gα AND SPARSE OPERATORS
The purpose of this paper is to check that the square function Gα, introduced by E. M. Stein in 1958, can be controlled by a finite sum of sparse operators when α > n+1 2 . This provides a usefulExpand