On the Hörmander classes of bilinear pseudodifferential operators II

2011/12/02 by Árpád Bényi, Frédéric Bernicot, Bényi, Árpad +7
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1112.0486

openalex publication_date 2011/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.

Citations

• Multilinear Calderón–Zygmund Theory
• On commutators of singular integrals and bilinear singular integrals
• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

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