In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L（logL）a（E1 × E2） for some a 〉 0, which is optimal.
In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absolutely continuous on(0,∞)and ‖m‖∞+sup j∈Z2j 2i+1 r|m′′(r)|dr<∞,then the multiplier defined by m(t)is bounded on Lpfor 2n/(n+3)
This paper is concerned with singular integral operators on product domains with rough kernels both along radial direction and on spherical surface. Some rather weaker size conditions, which imply the L^P-boundedness of such operators for certain fixed p （1 〈 p 〈 ∞）, are given.
