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 Lp-boundedness of such operators for certain fixed p(1 < p < ∞),are given.
