In this paper, the authors discuss a class of multilinear singular integralsand obtain that the operators are bounded from H^1 (R^n) to weak L^1 (R^n). Using this result, wecan directly prove a main theorem in [5].
The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)...The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)(S^(n-1))is a sufficient condition such that the κ-th order commutator is bounded on L^2(R^n).展开更多
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$is considered, whereQ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(A^n). A sufficient condition based on the Fourier transform estimate and implying the L^2(A^n) boundedness for the multilinear operator TA is given.展开更多
基金supported by Professor Xu Yuesheng's research grant in the program of "One hundred Distinguished Young Scientists"of the Chinese Academy of Sciences.
文摘In this paper, the authors discuss a class of multilinear singular integralsand obtain that the operators are bounded from H^1 (R^n) to weak L^1 (R^n). Using this result, wecan directly prove a main theorem in [5].
基金supported by the NSF of China(19701039)partially supported by the NFS of China(19971010)Visiting Scholar Foundation of Key Lab.in Peking University
文摘The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)(S^(n-1))is a sufficient condition such that the κ-th order commutator is bounded on L^2(R^n).
文摘The L^2(A^n) boundedness for the multilinear singular integral operators defined by$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.
