  Born-Jordan operators are a class of pseudodifferential operators arising as
a generalization of the quantization rule for polynomials on the phase space
introduced by Born and Jordan in 1925. The weak definition of such operators
involves the Born-Jordan distribution, first introduced by Cohen in 1966 as a
member of the Cohen class. We perform a time-frequency analysis of the Cohen
kernel of the Born -Jordan distribution, using modulation and Wiener amalgam
spaces. We then provide sufficient and necessary conditions for Born-Jordan
operators to be bounded on modulation spaces. We use modulation spaces as
appropriate symbols classes.
