# Acta Mathematica Sinica, English Series

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 1-16

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 17-46

*L*

^{2}-consistency of the estimates are established. The conditions employed involve the analogues of the Hardy–Littlewood maximal function. It is shown that the results are valid in particular for the...

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 123-134

*X, Y*are two real Banach Spaces. We know that for a standard

*∈*-isometry

*f*:

*X*→

*Y*, the weak stability formula holds and by applying the formula we can induce a closed subspace

*N*of

*Y**. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard

*∈*-isometry to be stable in assuming that

*N*is

*w**-closed in

*Y**. Making use of...

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 105-122

*P*

_{3}):

*αu*‴ (

*t*) +

*u*″(

*t*) =

*Au*(

*t*) +

*Bu*′ (

*t*) +

*Fu*

_{t}+

*f*(

*t*)(

*t*∈ $$\mathbb{T}$$ T := [0, 2π]) with periodic boundary conditions

*u*(0) =

*u*(2π),

*u*′(0) =

*u*′(2π),

*u*″ (0) =

*u*″(2π), in periodic Lebesgue–Bochner spaces

*L*

^{p}( $$\mathbb{T}$$ T ;

*X*) and periodic Besov spaces

*B*

_{p,q}

^{s}( $$\mathbb{T}$$ T ;...

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 135-160

_{t},

*t*∈ $$\mathfrak{T}$$ T } introduced in Li [

*Ann. Probab.*,

**42**, 41–79 (2014)], we construct a decreasing Lévy-CRT-valued process $$\left\{\mathfrak{T}_t,t\in\mathfrak{T}\right\}$$ { T t , t ∈ T } by pruning Lévy trees accordingly such that for each

*t*∈ $$\mathfrak{T}$$...

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 47-63

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 83-104

Acta Mathematica Sinica, English Series > 2019 > 35 > 1 > 64-82

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 245-256

*x*

_{n},

*y*

_{n}):

*n*∈ ℤ}, find a cardinal spline

*f*(

*x*), of a given degree, satisfying

*y*

_{n}=

*f*(

*x*

_{n}),

*n*∈ ℤ. Several necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 239-244

*X*to a compact nilmanifold

*Y*with $$X \geq \rm{dim}\it{Y}$$ X ≥ d i m Y . In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number

*N*(

*f*,

*g*) vanishes then

*f*and

*g*are deformable to be coincidence free. We also show that if

*X*is a connected finite complex

*X*and the Reidemeister...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 204-212

*G*be an extension of ℚ by a direct sum of

*r*copies of ℚ. (1) If

*G*is abelian, then

*G*is a direct sum of

*r*+ 1 copies of ℚ and Aut

*G*≅ GL(

*r*+ 1,

**Q**); (2) If

*G*is non-abelian, then

*G*is a direct product of an extraspecial ℚ-group

*E*and

*m*copies of ℚ, where

*E*/ζ

*E*is a linear space over

**Q**with dimension 2

*n*and

*m*+ 2

*n*=

*r*. Furthermore, let Aut

_{G′}

*G*be the normal subgroup of Aut

*G*consisting of all elements...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 185-203

*L*

^{Φ}to

*L*

^{φ}, where

*φ*denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function

*f*, closely related to the Calderón–Zygmund class

*t*

_{m}

^{p}(

*x*) which had been introduced in 1961. We also obtain weak and strong type inequalities...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 257-269

*X*be a compact metric space,

*F*:

*X*×ℝ →

*X*be a continuous flow and

*x*∈

*X*a proper quasi-weakly almost periodic point, that is,

*x*is quasi-weakly almost periodic but not weakly almost periodic. The aim of this paper is to investigate whether there exists an invariant measure generated by the orbit of

*x*such that the support of this measure coincides with the minimal center of attraction of

*x*? In...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 227-238

*m*, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its (0, λ)-Berezin transform on the boundary. In addition,...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 161-171

*G*) only in terms of a given degree sequence which is also related to the Euler characteristic. It has many important combinatorial applications in graph theory and gives direct information compared to the better known Euler characteristic on the realizability, connectedness, cyclicness, components, chords, loops etc. Many similar classification...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 270-296

*δ*(

*x*). In this way we obtain an estimated function with parameter

*β*. Secondly, the empirical likelihood method is developed to estimate the parameter

*β*. An estimated empirical log-likelohood...

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 172-184

Acta Mathematica Sinica, English Series > 2019 > 35 > 2 > 213-226

Acta Mathematica Sinica, English Series > 2019 > 35 > 3 > 369-377

*p*and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod

*p*, and give a sharp asymptotic formula for it.

Acta Mathematica Sinica, English Series > 2019 > 35 > 3 > 378-390

*R*be a ring,

*M*be a

*R*-bimodule and

*m*,

*n*be two fixed nonnegative integers with

*m*+

*n*≠ 0. An additive mapping

*δ*from

*R*into

*M*is called an (

*m*,

*n*)-

*Jordan derivation*if (

*m*+

*n*)

*δ*(

*A*

^{2}) = 2

*mAδ*(

*A*) + 2

*nδ*(

*A*)

*A*for every

*A*in

*R*. In this paper, we prove that every (

*m*,

*n*)-Jordan derivation with

*m*≠

*n*from a

*C** -algebra into its Banach bimodule is zero. An additive mapping

*δ*from

*R*into

*M*is called a (

*m*,

*n*)-...