Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a loca...Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a local Musielak-Orlicz Hardy space h￠（Nn） by the local grand maximal function, and a local BMO-type space bmo￠（Nn） which is further proved to be the dual space of h￠（Nn）. As an application, the authors prove that the class of pointwise multipliers for the local BMO-type space bmo￠（Nn）, characterized by Nakai and Yabuta, is just the dual of LI（Rn） ＋ hФ0 （Rn）, where Ф is an increasing function on （0, co） satisfying some additional growth conditions and Ф0 a Musielak-Orlicz function induced by Ф. Characterizations of h￠（Rn）, including the atoms, the local vertical and the local nontangential maximal functions, are presented. Using the atomic char- acterization, the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of h￠（Rn）, from which, the authors further deduce some criterions for the boundedness on h￠（Rn） of some sublinear operators. Finally, the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on h￠（Rn）.展开更多
The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of ...The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.展开更多
Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth m...Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.展开更多
This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-...This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.展开更多
We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We const...We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.展开更多
This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), co...This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), complete results are obtained.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11171027)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘Let￠ ： Nn x [0,∞） -4 [0, ∞） be a function such that ￠（x,.） is an Orlicz function and ￠（.,t） ∈ Aloc∞（Nn） （the class of local weights introduced by Rychkov）. In this paper, the authors introduce a local Musielak-Orlicz Hardy space h￠（Nn） by the local grand maximal function, and a local BMO-type space bmo￠（Nn） which is further proved to be the dual space of h￠（Nn）. As an application, the authors prove that the class of pointwise multipliers for the local BMO-type space bmo￠（Nn）, characterized by Nakai and Yabuta, is just the dual of LI（Rn） ＋ hФ0 （Rn）, where Ф is an increasing function on （0, co） satisfying some additional growth conditions and Ф0 a Musielak-Orlicz function induced by Ф. Characterizations of h￠（Rn）, including the atoms, the local vertical and the local nontangential maximal functions, are presented. Using the atomic char- acterization, the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of h￠（Rn）, from which, the authors further deduce some criterions for the boundedness on h￠（Rn） of some sublinear operators. Finally, the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on h￠（Rn）.
基金Project supported by the State Education Commission, the 973 Project "Nonlinear Science" the National Natural Science Foundation of China (No.9725104, No.19971084).
文摘The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.
基金This research was supported by the National Basic Research Program of China （Grant No. 2007CB209603）, Key Project of the National Natural Science Foundation （Grant No. 40830424）, State Key Laboratory of Geological Processes and Mineral Resources Geo-detection Laboratory of the Ministry of Education for their sponsorship （GPMR 200633, GDL0801）.
文摘Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.
基金supported by the National Natural Science Foundation of China(No.11101121)
文摘This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions.By using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.
基金supported by National Science Foundation of USA (Grant No. DMS1408839)a McDevitt Endowment Fund at Georgetown University
文摘We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.
文摘This paper continues the studies of the essential spectrum Of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativisticSchredinger operator, ￣ + v(x), complete results are obtained.
