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Acta Mathematica Sinica,Chinese Series
2017, Vol.33 Num.10
Online: 2017-10-15

1297 Youngsoo SEOL
Moderate Deviations for Marked Hawkes Processes

We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu[Stoch. Models, 31, 433-451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes.

2017 Vol. 33 (10): 1297-1304 [Abstract] ( 5 ) [HTML 1KB] [PDF 184KB] ( 14 )
1305 Huan Huan LI
Two Acyclicizations of a Complex and an Explicit Recollement

By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes.

2017 Vol. 33 (10): 1305-1320 [Abstract] ( 3 ) [HTML 1KB] [PDF 253KB] ( 11 )
1321 Tao CHENG, Hui Qiang SHI, Shanshuang YANG
Sewing Homeomorphism and Conformal Invariants

This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.

2017 Vol. 33 (10): 1321-1338 [Abstract] ( 7 ) [HTML 1KB] [PDF 239KB] ( 23 )
1339 Jian Ping ZHANG, Yun Zhang LI
On a Class of Weak Nonhomogeneous Affine Bi-frames for Reducing Subspaces of L2(Rd)

For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L2(Rd), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.

2017 Vol. 33 (10): 1339-1351 [Abstract] ( 3 ) [HTML 1KB] [PDF 245KB] ( 7 )
1352 Liang JIN, Xiaojun CUI
Weak Solutions on Lorentzian 2-tori

In this paper, we classify the set of Lorentzian metrics on T2, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations.

2017 Vol. 33 (10): 1352-1360 [Abstract] ( 6 ) [HTML 1KB] [PDF 212KB] ( 9 )
1361 Xing Xiao LI, Hong Ru SONG
Regular Space-like Hypersurfaces in S1m+1 with Parallel Para-Blaschke Tensors

In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space S1m+1 with parallel para-Blaschke tensors.

2017 Vol. 33 (10): 1361-1381 [Abstract] ( 3 ) [HTML 1KB] [PDF 286KB] ( 12 )
1382 Pei MA, Feng Quan LI, Yan LI
A Pohozaev Identity for the Fractional Hénon System
In this paper, we study the Pohozaev identity associated with a Hénon-Lane-Emden system involving the fractional Laplacian:

in a star-shaped and bounded domain Ω for s ∈ (0, 1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases.
2017 Vol. 33 (10): 1382-1396 [Abstract] ( 3 ) [HTML 1KB] [PDF 231KB] ( 21 )
1397 Jing ZHANG, Huo Xiong WU
Weighted Oscillation and Variation Inequalities for Singular Integrals and Commutators Satisfying Hörmander Type Conditions

This paper is devoted to investigating the weighted Lp-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type (p, p) estimates for 1 < p < ∞ and the weighted weak type (1, 1) estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain Hörmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini's conditions as model examples. Meanwhile, we also obtain the weighted Lp-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO(Rd)-functions.

2017 Vol. 33 (10): 1397-1420 [Abstract] ( 3 ) [HTML 1KB] [PDF 317KB] ( 17 )
1421 Xin LUO, Ying Qing XIAO, Yue Ping JIANG
On the Asymptotically PT-1 Spaces

In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT-1 space are still an asymptotically PT-1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT-1 spaces under particular conditions, which provide some concrete examples of asymptotically PT-1 spaces.

2017 Vol. 33 (10): 1421-1430 [Abstract] ( 3 ) [HTML 1KB] [PDF 204KB] ( 12 )
1431 Rui Dong WANG, Xu Jian HUANG
Isometries and Additive Mapping on the Unit Spheres of Normed Spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.

2017 Vol. 33 (10): 1431-1442 [Abstract] ( 9 ) [HTML 1KB] [PDF 212KB] ( 14 )
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