Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

2019/12/12 by Akihiko Miyachi, Miyachi, Akihiko, Naoto Shida +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1912.06233

openalex publication_date 2019/12/12 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

In this paper, the L² × L^∞ → L² and L² × L² → L¹ boundedness of bilinear Fourier multiplier operators is discussed under weak smoothness conditions on multipliers. As an application, we prove the L² × BMO → L² and L² × L² → H¹ boundedness of bilinear operators with multipliers of limited smoothness satisfying vanishing conditions.

Citations

• A Hörmander type multiplier theorem for multilinear operators
• Multilinear Calderón–Zygmund Theory
• Hp spaces of several variables

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• Bilinear Fourier multipliers and the rate of decay of their derivatives
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• On some bilinear Fourier multipliers with oscillating factors, II
• On the bilinear square Fourier multiplier operators and related multilinear square functions