The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on th...The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on the unit sphere as well as in the radial direction. These results substan- tially improve and extend some known results.展开更多
Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the ke...Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels.展开更多
In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications o...In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.展开更多
In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding ...In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.展开更多
In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of t...In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.展开更多
The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral opera...The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.展开更多
Abstract In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a conseque...Abstract In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L（Sn-1）. Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.展开更多
讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)...讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)∈△γ(R+)={sup R-1 integral (|h(t)|γdt) from n=0 to R},γ>1,R>0,ω是某类径向权.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11071200,11371295)NSF ofFujian Province of China(Grant No.2010J01013)
文摘The Lp bounds for the parametric Marcinkiewicz integrals associated to compound mapq pings, which contain many classical surfaces as model examples, are given, where the kernels of our operators are rather rough on the unit sphere as well as in the radial direction. These results substan- tially improve and extend some known results.
文摘Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173)
文摘In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.
文摘In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.
基金Supported by National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province (Grant No. 2010J01013)
文摘In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.
基金Project supported by the National Natural Science Foundation of China (No. 10771110)the Major Project of the Ministry of Education of China (No. 309018)
文摘The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.
文摘Abstract In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space L log L（Sn-1）. Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.
文摘讨论了如下定义的带粗糙核的超奇异积分算子:TΩ,α,hf(x)=p.v.∫Rnh(|y|)(Ω(y′))/(|y|(n+a))f(x-y)dy的(Lαp(ω),Lαp(ω))有界性,推广了已有的结果.这里0≤α<1,1<p<∞,Ω为Hq(Sn-1)中的函数,q=(n-1)/(n-1+α),且h(|y|)∈△γ(R+)={sup R-1 integral (|h(t)|γdt) from n=0 to R},γ>1,R>0,ω是某类径向权.
