A Restriction Theorem on the Reduced Product Heisenberg Group

In this paper,we give the Plancherel formula on the reduced product Heisenberg group,and obtain a restriction theorem on this group.

On Chevalley Restriction Theorem for Semi-reductive Algebraic Groups and Its Applications

An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical.Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular representations of non-classical finite-dimensional simple Lie algebras in positive characteristic,and some other cases.Let G be a connected semi-reductive algebraic group over an algebraically closed field F and g=Lie(G).It turns out that G has many same properties as reductive groups,such as the Bruhat decomposition.In this note,we obtain an analogue of classical Chevalley restriction theorem for g,which says that the G-invariant ring F[g]~G is a polynomial ring if g satisfies a certain“positivity”condition suited for lots of cases we are interested in.As applications,we further investigate the nilpotent cones and resolutions of singularities for semi-reductive Lie algebras.

A restriction theorem for oscillatory integral operator with certain polynomial phase

We consider the oscillatory integral operator Ta,mf（X） f（y）dy, where the function f is a Schwartz function.In this paper, the restriction theorem on Sn-1 for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem.

A Restriction Theorem Associated with the Generalized Sublaplacian

In this paper,we investigate the generalized Sublaplacian.We give the expression of the restriction operators explicitly.By introducing the generalized λ-twisted convolutions,we obtain the estimates of the restriction operators in the mixed L^P spaces.Finally,we get a restriction theorem associated with the generalized Sublaplacian.

A Study Guide for the l^2 Decoupling Theorem

This paper contains a detailed, self contained and more streamlined proof of the l^2 decoupling theorem for hypersurfaces from the paper of Bourgain and Demeter in 2015. The authors hope this will serve as a good warm up for the readers interested in understanding the proof of Vinogradov's mean value theorem from the paper of Bourgain,Demeter and Guth in 2015.

Riesz potentials of Hardy-Hausdorff spaces and Q-type spaces

This study investigates the restriction problem for the Riesz potentials of Hardy-Hausdorff spaces HH^1-γ(R^n)and Q-type spaces Qγ(R^n).By exploiting a geometric-measure theory generated by the indicatorlike functions of compact sets,it is proved that the Riesz operator Iαcontinuously maps HH^1-γ(R^n)into the weak Morrey spaces L^q,λ/μ,*induced by a Radon measureμ,which obeys a geometric condition.