BOUNDEDNESS OF COMMUTATORS ON HOMOGENEOUS MORREY-HERZ SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ （G） named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups

CONTINUITY OF MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS MORREY-HERZ SPACES

Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.

CBMO ESTIMATES FOR MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS MORREY-HERZ SPACES

The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b（x） ∈ CBMOq （Rn） on homogeneous Morrey-Herz spaces is established.

Boundedness for Multilinear Commutators of Marcinkiewicz Integral on Morrey-Herz Spaces with Non Doubling Measures

In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO（μ） function on homogeneous Morrey-Herz spaces with non doubling measures.

Boundedness of Multilinear Commutators with Rough Kernels on Morrey-Herz Spaces

This paper is concerning the commutators generated by the multilinear singular integral with rough kernels and BMO functions. The boundedness of the multilinear commutators Tb→ （f→） is established on the Morrey-Herz space by using the John-Nirenberg inequality.

Boundedness of Some Singular Integral Operators on Morrey-Herz Spaces over Locally Compact Vilenkin Groups

In this paper the boundedness results for some fractional and singular integral operators on the homogeneous Morrey-Herz spaces over locally compact Vilenkin groups are shown.

BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f )is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H~2(Ω) of other pseudoconvex domains.In these arguments,Amar's L~p-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H~p(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES

We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.

Identity of Urban Spaces: Assessment and Evaluation

As a major symbol of civilization,the city was built by man for his security and comfort.It is not only a settlement,but also an urban development which has been identified with the spirit that has been breathed into the community.Urban identity which is also known as collective identity,has gained meaning through the content of objective manifestation and the creation of flashbacks,citizens’memories and mental associations.That is what makes urban dwellers become citizens.Although the identity of the city is a result of civic culture,it still has an influence on the process of citizenship and can also be a reason for developing criteria related to the participation and assessment of its inhabitants.According to the view that identity is a set of traits and characteristics that distinguishes the dignity of a person and a society from other individuals and communities,a city becomes characterized and independent by adhering to these criteria.Despite the importance of identity as one of the richest qualitative aspects of urban life that gives meaning and fulfilment to the human quiddity,this complicated and expanded concept has still not been seriously considered,especially in relation to urban spaces.In fact,identity in architecture and urban spaces has recently diminished,since the main focus lies on building spaces for optimized profit and not for high quality living areas.In this research paper,parameters affecting urban identity are evaluated,and strategies and guidelines to promote these parameters are finally presented.

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

Attributes of Domestic Spaces for Contemporary Habitation-A Secondary Publication

The domestic space can be defined as the sphere that articulates the needs for subjective containment and contextual stimuli.In this sense,questions arise about the indispensable attributes that spaces must possess for this articulation to take place adequately.Architecture,as the discipline in charge of satisfying the specific spatial needs of those who inhabit these spaces and,in a broader sense,as a concrete contribution to society,must address this relationship in all its complexity and generate concrete responses that incorporate the appropriate spatial attributes during the design processes.The design processes that shape living spaces confront this dialectic,and the manner in which they do so brings identity and character to them.It is believed that the higher the level of variables that are contemplated and weighted,the greater the adequacy of spaces to the changing dynamics of the people who inhabit them.This article focuses on a thorough analysis of these spatial attributes,in parallel to the definition of each one as a particular condition for design,based on their conceptualization,breakdown,and articulation.Conceptually,the following attributes are addressed:flexibility,adaptability,variability,versatility,multiplicity,plurality,integrality,gradualness,incrementality,progressiveness,independence,connectivity,intimacy,and privacy.Each of these attributes is valued as a contribution to creating adequate habitability in contextual terms,with consideration to possible integrations and combinations.

Interactive Media Visual Interpretation of Traditional Chinese Graphics in Urban Public Spaces

This paper focuses on the application of interactive media technology in the visual interpretation of traditional graphic urban public spaces in China.Case studies and practical exploration show that interactive media technologies such as projection mapping,interactive devices,virtual reality technology,etc.,have realized the diversity of traditional graphics display forms in urban public space.The rich interactive experience design enhances the sense of participation and experience of urban citizens and tourists and promotes the visual culture transmission of traditional Chinese graphics.The future urban public space exhibition is destined to continue to deepen the integration of technology and graphics,promote the visual communication of traditional Chinese graphics visual interpretation in urban public space,and promote sustainable innovation in cultural output in urban public space exhibitions around the world.

Boundedness of Some Operators and Commutators in Morrey-Herz Spaces on Non-Homogeneous Spaces

The authors introduce the homogeneous Morrey-Herz spaces and the weak homo- geneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in ho- mogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators,Calderón-Zygmund operators and fractional integral operators.Further- more,some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained.Moreover,the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calderón-Zygmund operators or fractional integral operators with RBMO（μ）functions.

3D MERGE与3D SPACE STIR序列在腰椎间盘突出症检查中的应用比较

目的:对比三维多回波恢复梯度回波(3D MERGE)、三维可变反转角快速自旋回波(3D SPACE STIR)序列在腰椎间盘突出症(LDH)检查中的应用效果。方法:选择2020年1月~2022年11月收治的135例LDH患者,回顾性分析患者临床和磁共振成像(MRI)资料,所有患者均接受常规MRI扫描及3D MERGE、3D SPACE STIR序列扫描,对比3D MERGE、3D SPACE STIR序列测量神经根直径的一致性,评价两种序列的图像质量参数[信噪比(SNR)、对比噪声比(CNR)]、图像清晰度评分。结果:3D MERGE和3D SPACE STIR序列测量的L3~S1神经根直径比较差异无统计学意义(P>0.05),且两组序列测量的L3、L4、L5和S1直径均显示出较高相关性(r=0.957,0.986,0.975,0.972,P<0.05);3D MERGE序列的SNR及CNR均高于3D SPACE STIR序列,神经根显示分级、图像清晰度评分优于3D SPACE STIR序列,差异有统计学意义(P<0.05)。结论:3D MERGE、3D SPACE STIR序列在LDH神经根直径测量中具有极高一致性,3D MERGE序列较3D SPACE STIR序列能够更清晰显示神经跟的解剖形态,图像质量更好。

基于Conceptual Play Spaces理论的初中语文教育游戏设计

在真实的情境中教学可以促进学生的理解,对于初中生来说,他们需要一些具体形象的支撑,3D体验游戏可以将抽象的事物具体化,让学生感受到真实的世界。本文以Conceptual Play Spaces理论为基础,根据初中生的学习特征,设计教育游戏桃花源记,激发学习者的学习兴趣,使学生沉浸在教育游戏情境中,提高学习者核心素养。