The complete boundedness of singular integrals on weighted flag and product Hardy space

It is known that product singular integrals are bounded on product Hardy spaces and that flag singular integrals are bounded on flag Hardy spaces. The purpose of this paper is to obtain the complete boundedness of singular integrals on weighted flag and product Hardy spaces. In particular, we prove the boundedness of one-parameter singular integrals on both weighted flag and product Hardy spaces, as well as the boundedness of flag singular integrals on weighted product Hardy spaces.