In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley...In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.展开更多
In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the...In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the virtual count of X by symmetric semi-perfect obstruction theories.As an application,we prove that Joyce’s d-critical scheme admits a symmetric semi-perfect obstruction theory,which can be applied to the virtual Euler characteristics by Jiang-Thomas.展开更多
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
文摘In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
文摘In this paper we survey some results on the symmetric semi-perfect obstruction theory on a Deligne-Mumford stack X constructed by Chang-Li,and Behrend’s theorem equating the weighted Euler characteristic of X and the virtual count of X by symmetric semi-perfect obstruction theories.As an application,we prove that Joyce’s d-critical scheme admits a symmetric semi-perfect obstruction theory,which can be applied to the virtual Euler characteristics by Jiang-Thomas.
