Bilinear square spectral multipliers on stratified groups

Abstract

In this paper, on stratified groups, we give a reasonable definition of bilinear square spectral multiplier and its commutator. Then we study their boundedness on weighted Lebesgue spaces under the assumption of its weak boundedness and a sum-type Hormander condition. Besides, we show that, in Euclidean spaces, the smoothness conditions applied to ensure the boundedness of bilinear square Fourier multiplier can be replaced by the sum-type Hormander condition.