Research on Fourier integrals of several variables

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(1) We proved the weighted weak type (1,1) estimates both for the Calderon-Zygmund type singular integrals and for the Littlewood-Paley functions. These operators are defined by certain rough kernels.(2) We proved some weighted estimates for the Littlewood-Paley functions on the weighted Hardy spaces. Also some weighted estimates for the generalized Bochner-Riesz operators and for the generalized spherical means are obtained.(3) For certain classes of pseudo-differential operators, we proved L^2_w - L^2_w, L^1_w - L^<1,∽>_w and H^1_w - L^1_w estimates.(4) We proved the L^p estimates for certain singular integrals associated to the variable surface of revolution.(5) We studied certain multilinear Littlewood-Paley functions arising from rough kernels.(6) We proved the weak type (1,1) estimates for the Marcinkiewicz integrals by assuming for the kernel the LlogL condition on the unit sphere S^<n-1>.(7) 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.(8) 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.(9) 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 surface of revolution, both with H^1 kernels.