In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing funct...In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.展开更多
In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding ...In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.展开更多
基金Supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20220324)Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.22KJB110016)。
文摘In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.
基金Supported by National Natural Science Foundation of China(Grant No.11171345)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)the State Scholarship Fund of China
文摘In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.
