Research on Fourier integrals of several variables

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(1) We proved the weak type (1,1) estimates for the Marcinkiewicz integrals by assuming for the kernel the L log L condition on the unit sphere S^<n-1>.(2) We proved the A_1-weighted weak (1,1) estimates for the oscillatory singular integrals of polynomial phase arising from the smooth kernels.(3) We proved the weighted weak (1,1) estimate for the oscillatory singular integrals of polynomial phase with the rough kernels satisfying certain Dini conditions, assuming for the weights the conditions corresponding to the Dini conditions.(4) We proved transference theorems between the multilinear multiplier operators on the Euclid space R^n and the ones on the torus T^n. Also we obtained some applications of these results.(5) We proved transference theorems for the L^P, the weak L^P and H^P-L^P estimates between the Littlewood-Paley functions on the Euclid space R^n and those on the torus T^n. Also we obtained some applications of these results.(6) We proved the L^P estimates for the Littlewood-Paley functions along curves and the related singular integrals, both arising from the rough kernels. As applications, we proved the L^P estimates for the Marcinkiewicz integrals along curves and the singular integrals associated to the surfaces of revolutions, both with H^1 kernels.