In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.
In this paper,a weak type(1,1)estimate is established for the higher order commutator introduced by Christ and Joume which is defined byT[a1,…,a1]f(x)=p.v∫R^dK(x-y)(lПi=1 mx,yai)·f(y)dy,where K is the standard...In this paper,a weak type(1,1)estimate is established for the higher order commutator introduced by Christ and Joume which is defined byT[a1,…,a1]f(x)=p.v∫R^dK(x-y)(lПi=1 mx,yai)·f(y)dy,where K is the standard Calderon-Zygmund convolution kernel on R^d(d≥2)and mx,yai=∫0^1ai(sx+(1-s)y)ds.展开更多
We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.
It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if The paper partially solves this conjecture. In the same time, the paper also discusses...It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if The paper partially solves this conjecture. In the same time, the paper also discusses the volume growth of a manifold with asymptotically nonnegative Ricci curvature.展开更多
文摘In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.
基金supported by NSFC (Nos. 11871096, 11801118 and No. 11571160)China Postdoctoral Science Foundation (No. 2017M621253 and No. 2018T110279)the Fundamental Research Funds for the Central Universities
文摘In this paper,a weak type(1,1)estimate is established for the higher order commutator introduced by Christ and Joume which is defined byT[a1,…,a1]f(x)=p.v∫R^dK(x-y)(lПi=1 mx,yai)·f(y)dy,where K is the standard Calderon-Zygmund convolution kernel on R^d(d≥2)and mx,yai=∫0^1ai(sx+(1-s)y)ds.
基金Supported by the National Natural Science Foundation of China(11701403).
文摘We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.
文摘It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if The paper partially solves this conjecture. In the same time, the paper also discusses the volume growth of a manifold with asymptotically nonnegative Ricci curvature.
