研究带粗糙核的振荡积分算子 Tf(x)=P.V.integral from n=R^n to e^(ip(x,g))Ω(x-y)|x-y|^(-1)f(y)dy,其中 P(xy)是R^n×R^n中的实多项式,Ω(x)是R^n中的零次齐次函数且在单位球面S^(n-1)的积分为零。通过适当的取值分解,证明了Ω...研究带粗糙核的振荡积分算子 Tf(x)=P.V.integral from n=R^n to e^(ip(x,g))Ω(x-y)|x-y|^(-1)f(y)dy,其中 P(xy)是R^n×R^n中的实多项式,Ω(x)是R^n中的零次齐次函数且在单位球面S^(n-1)的积分为零。通过适当的取值分解,证明了Ω∈Llog^+(S^(n-1))时,Tf(x)展开更多
In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degr...In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).展开更多
文摘研究带粗糙核的振荡积分算子 Tf(x)=P.V.integral from n=R^n to e^(ip(x,g))Ω(x-y)|x-y|^(-1)f(y)dy,其中 P(xy)是R^n×R^n中的实多项式,Ω(x)是R^n中的零次齐次函数且在单位球面S^(n-1)的积分为零。通过适当的取值分解,证明了Ω∈Llog^+(S^(n-1))时,Tf(x)
文摘In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).
