The L^2(A^n) boundedness for the multilinear singular integral operators defined by$T_A f\left( x \right) = \int_{Ropf^n } {{{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + 1} }}} \left( {A\left( x ...The L^2(A^n) boundedness for the multilinear singular integral operators defined by$T_A f\left( x \right) = \int_{Ropf^n } {{{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + 1} }}} \left( {A\left( x \right) - A\left( y \right) - \nabla A\left( y \right)\left( {x - y} \right)} \right)f\left( y \right)dy$is considered, whereQ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(A^n). A sufficient condition based on the Fourier transform estimate and implying the L^2(A^n) boundedness for the multilinear operator TA is given.展开更多
文摘The L^2(A^n) boundedness for the multilinear singular integral operators defined by$T_A f\left( x \right) = \int_{Ropf^n } {{{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + 1} }}} \left( {A\left( x \right) - A\left( y \right) - \nabla A\left( y \right)\left( {x - y} \right)} \right)f\left( y \right)dy$is considered, whereQ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(A^n). A sufficient condition based on the Fourier transform estimate and implying the L^2(A^n) boundedness for the multilinear operator TA is given.
