Notes on the spaces of bilinear multipliers

2009/05/26 by Óscar Blasco, Blasco, Oscar
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0905.4151

openalex publication_date 2009/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A locally integrable function m(ξ,η) defined on \mathbb Rⁿ× \mathbb Rⁿ is said to be a bilinear multiplier on \mathbb Rⁿ of type (p₁,p₂, p₃) if B_m(f,g)(x)=∫_{\mathbb Rⁿ} ∫_{\mathbb Rⁿ} f(ξ) g(η)m(ξ,η)e^2πi( dξdη defines a bounded bilinear operator from L^p₁(\mathbb Rⁿ)× L^p₂(\mathbb Rⁿ) to L^p₃(\mathbb Rⁿ). The study of the basic properties of such spaces is investigated and several methods of constructing examples of bilinear multipliers are provided. The special case where m(ξ,η)= M(ξ-η) for a given M defined on \mathbb Rⁿ is also addressed.

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