1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. I...1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:展开更多
In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfi...In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.展开更多
In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic co...In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic corrections to it,（-△+m<sup>2</sup>）<sup>1/2</sup>+v（x）,v（x）→-∞,as|x|→∞.展开更多
In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-...In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.展开更多
Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitatire representation of uncertainty principle.
In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichart...In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal展开更多
The type changed operators are introduced in this paper. A regular cauchy problem for a class of singular hyperbolic equations are considered. Existence and uniqueness of the solution of the problem can be proved.
Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ）...Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ） of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0（F） and Fpq^0（F）.展开更多
In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic ca...In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.展开更多
基金Project supported by the Science Fund of the Chinese Academy of Sciences.
文摘1. Introduction In application of nonlinear boundary value problems, it is sometimes important to know that L~2-boundedness of a class of pseudo-differential operators with symbols whioh have nonsmooth coefficients. In [2], Coifman and Meyer proved that the operator σ(x, D) is bounded in L~2(R~n) if its symbold (x, ξ) satisfies:
基金Supported partially by the National Natural Science Foundation of China(Grant No.11371200)the Research Fund for the Doctoral Program of Higher Education(Grant No.20120031110023)
文摘In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights.
文摘In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic corrections to it,（-△+m<sup>2</sup>）<sup>1/2</sup>+v（x）,v（x）→-∞,as|x|→∞.
基金Xu Jingshi was partially supported by NSF of Hunan in ChinaYang DaChun was partially supported by NNSF(10271015)and SEDF of China
文摘In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.
文摘Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitatire representation of uncertainty principle.
基金Supported by the National Natural Science Foundation of China the Doctoral Foundation of NEM of China
文摘In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal
文摘The type changed operators are introduced in this paper. A regular cauchy problem for a class of singular hyperbolic equations are considered. Existence and uniqueness of the solution of the problem can be proved.
基金The author is partially supported by NNSF(10271015) RFDP(20020027004)of China
文摘Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ） of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0（F） and Fpq^0（F）.
文摘In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.
