Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimate...Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.展开更多
This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is ...This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.展开更多
文摘Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.
基金supported by Grant-in-Aid for Young Scientists(B)(Grant No.23740106)
文摘This paper aims to introduce some new ideas into the study of submodules in Hilbert spaces of analytic functions. The effort is laid out in the Hardy space over the bidisk H^2(D^2). A closed subspace M in H^2(D^2) is called a submodule if ziM ? M(i = 1, 2). An associated integral operator(defect operator) CM captures much information about M. Using a Kre??n space indefinite metric on the range of CM, this paper gives a representation of M. Then it studies the group(called Lorentz group) of isometric self-maps of M with respect to the indefinite metric, and in finite rank case shows that the Lorentz group is a complete invariant for congruence relation. Furthermore, the Lorentz group contains an interesting abelian subgroup(called little Lorentz group) which turns out to be a finer invariant for M.
