Research on Fourier integrals of several variables

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(1)We proved the pointwise relations between some multiparameter square functions on R^n, and we applied them to prove H^p - L^p and L(log L)^<n-1> - L^<1, *> estimates for multiparameter Marcinkiewicz integrals. To show the weak type estimate, we also proved a resonance theorem on Orlicz spaces.(2)We proved that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on L^p_ 1 <p < *, w * A_p (the weights of Muckenhoupt). The kernels are satisfying only size and cancellation conditions. Then, we gave some applications to the Carleson measures on the upper half space.