Estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents

Abstract

Abstract In this paper, we give Leibniz-type estimates of bilinear pseudodifferential operators associated to bilinear Hörmander classes in Besov and Triebel–Lizorkin spaces with variable exponents. To obtain the estimate for Triebel–Lizorkin spaces with variable exponents, we present their approximation characterization.

Keywords

• Variable exponent
• Triebel–Lizorkin space
• Besov space
• Bilinear pseudodifferential operator