Bilinear Bochner-Riesz square function and applications
Surjeet Singh Choudhary, K. Jotsaroop, Saurabh Shrivastava, Kalachand, Shuin

TL;DR
This paper introduces a bilinear Stein's square function related to Bochner-Riesz means, explores its $L^p$ boundedness, and applies it to bilinear multipliers, maximal functions, and fractional Schr"odinger multipliers, extending previous results.
Contribution
It develops a new bilinear Stein's square function, establishes its $L^p$ bounds, and applies it to various bilinear multiplier problems, including maximal functions and fractional Schr"odinger operators.
Findings
Established $L^p$ boundedness of the bilinear Stein's square function.
Derived $L^p$ estimates for bilinear fractional Schr"odinger multipliers.
Provided a dimension-free condition for $L^2 imes L^2 o L^1$ boundedness of bilinear maximal functions.
Abstract
In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and investigate its boundedness properties. Further, we discuss several applications of the square function in the context of bilinear multipliers. In particular, we obtain results for maximal function associated with generalised bilinear Bochner-Riesz means. This extends the results proved in~\cite{JS}. Another application concerns the estimates for bilinear fractional Schr\"{o}dinger multipliers. Finally, we improve upon a result of Grafakos, He and Honzik~\cite{GHH} in the context of bilinear radial multipliers and provide a dimension free sufficient condition on the bilinear multipliers for boundedness of the associated maximal function. The generalised bilinear spherical maximal function is a particular example of such maximal functions.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Advanced Mathematical Physics Problems
