15 August 2014, Volume 30 Issue 8

    

• Select all
  |

Articles
• Select
  Weighted Estimates for Multilinear Pseudodifferential Operators

  Kang Wei LI, Wen Chang SUN

  Acta Mathematica Sinica. 2014, 30(8): 1281-1288. https://doi.org/10.1007/s10114-014-3027-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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 A_p weights to multiple weights.
• Select
  Trigonometric Series with a Generalized Monotonicity Condition

  Lei FENG, Vilmos TOTIK, Song Ping ZHOU

  Acta Mathematica Sinica. 2014, 30(8): 1289-1296. https://doi.org/10.1007/s10114-014-3496-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.
• Select
  Complex Interpolation of Weighted Besov and Lizorkin-Triebel Spaces

  Winfried SICKEL, Leszek SKRZYPCZAK, Jan VYBÍRAL

  Acta Mathematica Sinica. 2014, 30(8): 1297-1323. https://doi.org/10.1007/s10114-014-2762-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights w₀, w₁ are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calderón products of associated sequence spaces. Finally, as a corollary of these investigations, we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin-Triebel spaces on R^d.
• Select
  Tingley's Problem on Symmetric Absolute Normalized Norms on R²

  Ryotaro TANAKA

  Acta Mathematica Sinica. 2014, 30(8): 1324-1340. https://doi.org/10.1007/s10114-014-3491-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study Tingley's problem on symmetric absolute normalized norms on R². We construct new methods for Tingley's problem on two-dimensional spaces by using isosceles orthogonality, which does not make use of the notion of natural extension. Furthermore, using our methods, several sufficient conditions for Tingley's problem on symmetric absolute normalized norms on R² are given. As applications, we present various new examples including the two-dimensional Lorentz sequence space d⁽²⁾(ω, q) and its dual d⁽²⁾(ω, q)^* by simple arguments.
• Select
  Non-differentiability of Alpha Function at the Boundary of Flat

  Jian Lu ZHANG, Min ZHOU

  Acta Mathematica Sinica. 2014, 30(8): 1341-1352. https://doi.org/10.1007/s10114-014-3134-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  With the variational method introduced by Mather, we construct a mechanical Hamiltonian system whose α function has a flat F and is non-differentiable at the boundary ∂F. In the case of two degrees of freedom, we prove that this phenomenon is stable under perturbations of Mañé's.
• Select
  On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach Spaces

  Andrew ROSALSKY, Le Van THANH, Nguyen Thi THUY

  Acta Mathematica Sinica. 2014, 30(8): 1353-1364. https://doi.org/10.1007/s10114-014-3507-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  For a double array of independent random elements {V_mn,m≥1, n≥1} in a real separable Banach space, conditions are provided under which the weak and strong laws of large numbers for the double sums ∑_i=1^m ∑_j=1ⁿ V_ij , m≥1, n≥1 are equivalent. Both the identically distributed and the nonidentically distributed cases are treated. In the main theorems, no assumptions are made concerning the geometry of the underlying Banach space. These theorems are applied to obtain Kolmogorov, Brunk-Chung, and Marcinkiewicz-Zygmund type strong laws of large numbers for double sums in Rademacher type p (1≤p≤2) Banach spaces.
• Select
  Duals of Hardy Spaces of B-valued Martingales for 0<r≤1

  Lin YU

  Acta Mathematica Sinica. 2014, 30(8): 1365-1380. https://doi.org/10.1007/s10114-014-3611-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The dual of B-valued martingale Hardy space H ^_rs(p) (B) with small index 0<r≤1, which is associated with the conditional p-variation of B-valued martingale, is characterized. In order to obtain the results, a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.
• Select
  Uniform Exponential Attractor for Nonautonomous Partly Dissipative Lattice Dynamical System

  Sheng Fan ZHOU, Jia Jia LOU

  Acta Mathematica Sinica. 2014, 30(8): 1381-1394. https://doi.org/10.1007/s10114-014-1626-9

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces.
• Select
  Algebraic Properties of Toeplitz and Small Hankel Operators on the Harmonic Bergman Space

  Hong Yan GUAN, Yu Feng LU

  Acta Mathematica Sinica. 2014, 30(8): 1395-1406. https://doi.org/10.1007/s10114-014-3276-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C. We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator. Meanwhile, we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.
• Select
  Multilinear Fractional Hausdorff Operators

  Da Shan FAN, Fa You ZHAO

  Acta Mathematica Sinica. 2014, 30(8): 1407-1421. https://doi.org/10.1007/s10114-014-3552-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, by introducing the space with weak mixed norms, weak type estimates of two kinds of multilinear fractional Hausdorff operators RΦ, _β^→ and SΦ,_β on Lebesgue spaces are shown. By virtue of Marcinkiewicz interpolation, strong type estimates of these two operators on Lebesgue spaces are also obtained. Our methods shed some new light on dealing with the case of non-radial function Φ.
• Select
  Nonparametric Regression with Interval-Censored Data

  Wen Li DENG, Zu Kang ZHENG, Ri Quan ZHANG

  Acta Mathematica Sinica. 2014, 30(8): 1422-1434. https://doi.org/10.1007/s10114-014-0729-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In many medical studies, the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease. In nonparametric regression model, when the response variable is subjected to interval-censoring, the regression function could not be estimated by traditional methods directly. With the censored data, we construct a new response variable which has the same conditional expectation as the original one. Based on the new variable, we get a nearest neighbor estimator of the regression function. It is established that the estimator has strong consistency and asymptotic normality. The relevant simulation reports are given.
• Select
  Spherical f-Tilings by Two Noncongruent Classes of Isosceles Triangles-II

  Ana BREDA, Robert DAWSON, Patrícia RIBEIRO

  Acta Mathematica Sinica. 2014, 30(8): 1435-1464. https://doi.org/10.1007/s10114-014-3302-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this work, we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern. As it will be shown, this class is composed by two discrete families denoted by Em, m≥2, m ∈ N, Fk, k≥4, k ∈ N and two sporadic tilings denoted by G and H.
• Select
  A Kinematic Formula for Integral Invariant of Degree 4 in Real Space Form

  De Shuo JIANG, Jia Zu ZHOU, Fang Wei CHEN

  Acta Mathematica Sinica. 2014, 30(8): 1465-1476. https://doi.org/10.1007/s10114-014-1266-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, kinematic formulae in a real space form are investigated. A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained. The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.