It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces $L^{p_1 } \times L^{p_2 } \times \cdots \times L^{p_k } (\mathbb{R}^n )$ to t...It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces $L^{p_1 } \times L^{p_2 } \times \cdots \times L^{p_k } (\mathbb{R}^n )$ to the Hardy spacesH r , (? n ) and the weak Hardy spaceH r,∞ (? n . As an application of this result, the L p ,(? n ) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.展开更多
本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)...本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.展开更多
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 19131080) of ChinaDoctoral Programme Foundation of Institution of Higher Education (Grant No. 98002703) of China
文摘It is proved that a class of multilinear singular integral operators with homogeneous kernels are bounded operators from the product spaces $L^{p_1 } \times L^{p_2 } \times \cdots \times L^{p_k } (\mathbb{R}^n )$ to the Hardy spacesH r , (? n ) and the weak Hardy spaceH r,∞ (? n . As an application of this result, the L p ,(? n ) boundedness of a class of commutator for the singular integral with homogeneous kernels is obtained.
文摘本文研究了Marcinkiewicz积分交换子μΩ,b(f)(x)=(integral from n=0 to ∞|Fb,t(f)(x)|2 dt/t3)1/2, 其中Fb,t(f)(x)=integral from n=|x-y|≤t(Ω(x-y_/|x-y|n-1)b(x)-b(y)f(y)dy及b∈Λβ,证明了算子μΩ,b是Lp(Rn) 到Fβ,∞p(Rn)上的有界算子并且也是Lp(Rn)到Lq(Rn)上的有界算子.
