In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both...In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both, and let'T^(t(j)) he Tt's restriction on R^(dj), j=1, 2. Then T's L^2-boundedness follows from: T has WBP, and T^(t(j))(b_j)=0, where b_j is any pseudoaccretive function on R^(dj), j=1, 2.展开更多
In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action...In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we give a kind of T(b) Theorem on product domains. Roughly speaking, let T be a singular integral operator on R^(d_1)×R^(d_2), let T`t be T's transpose with respect to (x, u), or (y, v) or both, and let'T^(t(j)) he Tt's restriction on R^(dj), j=1, 2. Then T's L^2-boundedness follows from: T has WBP, and T^(t(j))(b_j)=0, where b_j is any pseudoaccretive function on R^(dj), j=1, 2.
基金supported by the National Natural Science Foundation of China(Grant.No.10301004)Basis Research Foundation of Beijing Institute of Technology(Grant No.200307A14).
文摘In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.
