Boundedness of bilinear multipliers whose symbols have a narrow support
Frédéric Bernicot,Pierre Germain +1 more
TL;DR: In this article, the authors studied the boundedness of bilinear multipliers whose symbol is narrowly supported around a curve (in the frequency plane) and obtained the optimal decay rate for exponents satisfying a sub-Holder scaling.
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Abstract: This work is devoted to studying the boundedness on Lebesgue spaces of bilinear multipliers on ℝ whose symbol is narrowly supported around a curve (in the frequency plane). We are looking for the optimal decay rate (depending on the width of this support) for exponents satisfying a sub-Holder scaling. As expected, the geometry of the curve plays an important role, which is described. This has applications to the bilinear Bochner-Riesz problem (in particular, boundedness of multipliers whose symbol is the characteristic function of a set), as well as to the bilinear restriction-extension problem.
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Improved bound for the bilinear Bochner–Riesz operator
TL;DR: In this paper, the authors improved the previously known bounds for the bilinear Bochner-Riesz operator by using a decomposition which relates the estimates for the BOR to the square function estimates of the classical BOR.
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Weighted Estimates for Bilinear Bochner-Riesz Means at the Critical Index
TL;DR: In this article, the authors established weighted estimates for the bilinear Bochner-Riesz operator at the critical index, where α =n-\frac {1}{2}$ with respect to biliniear weights.
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Multilinear Harmonic Analysis
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TL;DR: In this article, a multilinear analysis of operators that depend linearly on several functions by treating all inputs as variables and not just some as parameters is presented, based on multiple simultaneous decompositions.
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Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3
Frédéric Bernicot,Pierre Germain +1 more
TL;DR: In this article, the authors consider a bilinear interaction between two linear dispersive waves with a generic resonant structure, and derive an asymptotic equivalent of the solution for data in the Schwartz class.
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•Posted Content
Weighted estimates for Bilinear Bochner-Riesz means at the critical index.
TL;DR: In this paper, the authors established weighted estimates for the bilinear Bochner-Riesz operator at the critical index δ = n-\frac{1}{2} with respect to bilinearly weights.
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