Boundedness of bilinear pseudo-differential operators of S_0,0-type on L² × L²

2019/01/22 by Tomoya Kato, Akihiko Miyachi, Kato, Tomoya +3
Mathematics · #35S05 #42B15 #42B35 #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.1901.07237

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the known result that the bilinear pseudo-differential operators with symbols in the bilinear Hörmander class BS^-n/2_0,0(ℝⁿ) are bounded from L² × L² to h¹. We show that those operators are also bounded from L² × L² to L^r for every 1< r ≤ 2. Moreover we give similar results for symbol classes wider than BS^-n/2_0,0(ℝⁿ). We also give results for symbols of limited smoothness.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Multilinear Calderón–Zygmund Theory

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