A remark on the relationship 1/p = 1/p₁ + 1/p₂ for boundedness of bilinear pseudo-differential operators with exotic symbols

2021/01/26 by Tomoya Kato, Kato, Tomoya, Naoto Shida +1
Computer Science · Mathematics · #35S05 #42B15 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2101.10529

openalex publication_date 2021/01/26 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

We consider the bilinear pseudo-differential operators with symbols in the bilinear Hörmander classes BS_{ρ, ρ}^m, 0 < ρ< 1. In this paper, we show that the condition 1/p = 1/p₁ + 1/p₂ is necessary when we consider the boudnedness from H^p₁ × H^p₂ to L^p of those operators for the critical case.

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