On the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2\times L^2$

Abstract

In this paper, the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2\times L^2$ are determined in the framework of Besov spaces. Our result improves the $L^2\times L^2\to L^1$ boundedness of those operators with symbols in the bilinear Hörmander class $B{S}_{0,0}^m$.

arXiv comment17 pages. To appear in J. Funct. Anal

References in corpus (4)

• Boundedness of pseudo-differential operators of type (0,0) on Triebel-Lizorkin and Besov spaces
• Boundedness of multilinear pseudo-differential operators of $S_{0,0}$-type in $L^2$-based amalgam spaces
• Bilinear pseudo-differential operators with exotic symbols
• Bilinear pseudo-differential operators with exotic class symbols of limited smoothness

Cited by in corpus (1)

• Kato-Ponce type inequality for bilinear pseudo-differential operators of $S_{0,0}$-type in the scale of Besov spaces