Bilinear pseudo-differential operators with exotic symbols, II

2018/01/21 by Miyachi, Akihiko, Tomita, Naohito
#42B20 #42B30 #47G30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.06745

Abstract

The boundedness from H^p × L² to L^r, 1/p+1/2=1/r, and from H^p × L^∞ to L^p of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear Hörmander class BS^m_ρ,ρ, 0 ≤ ρ<1, of critical order m, where H^p is the Hardy space. This combined with the previous results of the same authors establishes the sharp boundedness from H^p × H^q to L^r, 1/p+1/q=1/r, of those operators in the full range 0< p, q ≤ ∞, where L^r is replaced by BMO if r=∞.

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