GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

Research on Types of Regional Eco-protection Space and Its Protection Countermeasures——A Case Study of Chongzuo City of Guangxi Province in China

Reasonable division of eco-protection space is a vital measure to coordinate the relationship between regional economic development and ecological protection,and to realize regional sustainable development.The paper has concluded the concept of regional eco-protection space which has been divided into ecological space of forbidding development and restricted development.It has discussed methods to divide regional eco-protection space and proposed protection countermeasures for regional eco-protection space.GIS has been adopted to divide eco-protection space of Chongzuo City.The eco-protection space of Chongzuo City covers an overall area of 5,833.94 km2,taking up 34.04% of the total area of Chongzuo City;ecological space of forbidding development covers an area of 1,555.35 km2,taking up 8.97%;the ecological space of restricted development covers an area of 4,344.59 km2,taking up 25.07%.Finally,the protection countermeasures for regional eco-protection space have been proposed.

KKM TYPE THEOREMS AND COINCIDENCE THEOREMS ON L-CONVEX SPACES

Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

TOEPLITZ-TYPE OPERATORS ON LEBESGUE SPACES

Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...

Composition-integral Type Operators from F（p, q, s） Spaces to Bloch-type Spaces

This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.

COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL

Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained.

Some New Theorems of Lipschitz Type Mappings in Cone Metric Spaces

In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.

Butterfly taxonomic and functional diversity in the urban green spaces of Hefei city

Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.

CHARACTERIZATION OF MAXIMAL OPERATORS IN ORLICZ-MORREY SPACES OF HOMOGENEOUS TYPE

. In this paper,the characterization of boundedness of Hardy-Littlewood maximal operators in Orlicz-Morrey spaces LΦφ（X,μ） of homogeneous type is founded.

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.

A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE

A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.

ON DIRICHLET TYPE SPACES AND α-BLOCH SPACES IN THE UNIT BALL OF C^n

In this paper, the authors study the inclusion relations between Dirichlet type spaces DΥT and α-Bloch spaces βα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods. Furthermore, they sharpen one of the results when Υ=n, which proves that a conjecture in [7] is true.

Boundedness for Hardy Type Operators on Herz Spaces with Variable Exponents

In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.

Balloon-based exposed payload designed for astrobiological research in Earth’s near space

Earth’s near space,located in the region between 20 and 100 km above sea level,is characterized by extreme conditions,such as low temperature,low atmospheric pressure,harsh radiation,and extreme dryness.These conditions are analogous to those found on the surface of Mars and in the atmosphere of Venus,making Earth’s near space a unique natural laboratory for astrobiological research.To address essential astrobiological questions,teams from the Chinese Academy of Sciences(CAS)have developed a scientific balloon platform,the CAS Balloon-Borne Astrobiology Platform(CAS-BAP),to study the effects of near space environmental conditions on the biology and survival strategies of representative organisms in this terrestrial analog.Here,we describe the versatile Biological Samples Exposure Payload(BIOSEP)loaded on the CAS-BAP with respect to its structure and function.The primary function of BIOSEP is to expose appropriate biological specimens to the harsh conditions of near space and subsequently return the exposed samples to laboratories for further analysis.Four successful flight missions in near space from 2019 to 2021 have demonstrated the high reliability and efficiency of the payload in communicating between hardware and software units,recording environmental data,exposing sample containers,protecting samples from external contamination,and recovering samples.Understanding the effects of Earth’s near space conditions on biological specimens will provide valuable insights into the survival strategies of organisms in extreme environments and the search for life beyond Earth.The development of BIOSEP and associated biological exposure experiments will enhance our understanding of the potential for life on Mars and the habitability of the atmospheric regions of other planets in the solar system and beyond.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.