With the help of the maximal function caracterizations of the Besov-type space Bs,τ p,q and the Triebel- Lizorkin-type space Fs,τ p,q, we present the atomic decomposition of these function spaces. Our results cover ...With the help of the maximal function caracterizations of the Besov-type space Bs,τ p,q and the Triebel- Lizorkin-type space Fs,τ p,q, we present the atomic decomposition of these function spaces. Our results cover the results on classical Besov and Triebel-Lizorkin spaces by taking T = 0.展开更多
Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed modul...Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.展开更多
The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. Th...The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.展开更多
A combination of rapid industrialization, economic development and urbanization has caused a series of issues such as resource shortages, ecosystem destruction, environmental pollution and tension between human needs ...A combination of rapid industrialization, economic development and urbanization has caused a series of issues such as resource shortages, ecosystem destruction, environmental pollution and tension between human needs and land conservation. In order to promote balanced development of human, resources, ecosystems, the environment, and the economy and society, it is vital to conceptualize ecological spaces, production spaces and living spaces. Previous studies of ecological-production-living spaces focused mainly on urban and rural areas; few studies have examined mountainous areas. The Taihang Mountains, a key area between the North China Plain and Beijing-Tianjin-Hebei area providing ecological shelter and the safeguarding of crucial water sources, suffer from increasing problems of fragile environment, inappropriate land use and tensions in the human-land relationship. However, studies of the ecological, production, and living spaces in the Taihang Mountains are still lacking. Therefore, this study, based on the concept of ecological-production-living spaces and using data from multiple sources, took the Taihang Mountains as the study area to build a functional land classification system for ecological-production-living spaces. After the classification system was in place, spatial distribution maps for ecological, production and living spaces were delineated. This space mapping not only characterized the present land use situation, but also established a foundation for future land use optimization. Results showed that the area of ecological space was 78,440 km^2, production space 51,861 km^2 and living space 6,646 km^2, accounting for 57.28%, 37.87% and 4.85% of the total area, respectively. Ecological space takes up the most area and is composed mainly of forests and grasslands. Additionally, most of the ecological space is located in higher elevation mountainous areas, and plays an important role in regulating and maintaining ecological security. Production space, mostly farmlands sustaining livelihoods inside and outside the region, is largely situated in lower elevation plains and hilly areas, as well as in low-lying mountainous basins. Living space has the smallest area and is concentrated mainly in regions with relatively flat terrain and convenient transportation for human settlements.展开更多
New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann surfaces.Except inclusions between these generalized spaces it is shown that the c...New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann surfaces.Except inclusions between these generalized spaces it is shown that the capacity Bloch space is a maximal space for them.展开更多
Central place theory is one of the two theoretical cornerstones of geography, yet it cannot be connected with other spatial structure models, fails to provide definite time-space parameter conditions, lacks an evoluti...Central place theory is one of the two theoretical cornerstones of geography, yet it cannot be connected with other spatial structure models, fails to provide definite time-space parameter conditions, lacks an evolutionary process model, and does not easily enable construction of a complete theoretical system of regional spatial structure. This paper gives an in-depth analysis of the process and mechanism for production and evolution of central places of different grades, and constructs an evolutionary model of the central place hierarchical system. The results of deduction, analysis and simulation show that production and evolution of the central place hierarchical system may be divided into five stages. These stages are the embryonic, formative, improvement, maturation, and advancement stages. Affected by spatial location and centricity, central places have obvious differences in scale and functional structures. There are great differences in the scale of same-grade central places. However, low-grade central places could have larger scales than high-grade central places, and the central places of a central location may form the agglomeration area of central places. Based on the hypothesis condition of an isotropic plain, the research shows that it is possible not only to form proportional functional structures of central places, but also to produce non-proportional scale structures of central places, and thus to complete the transformation from rationalistic deduction of spatial equilibrium mode to an explanation and demonstration of an unbalanced practical model.展开更多
In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as fu...In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Aφ1,w and Aφ2,w, and get the space of multipliers from the space Aφ1,w to the space Mφ2.w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Aφ,w^p,q.展开更多
文摘With the help of the maximal function caracterizations of the Besov-type space Bs,τ p,q and the Triebel- Lizorkin-type space Fs,τ p,q, we present the atomic decomposition of these function spaces. Our results cover the results on classical Besov and Triebel-Lizorkin spaces by taking T = 0.
基金supported by National Natural Science Foundation of China(Grant Nos.11171015 and 11301568)
文摘Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.
文摘The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.
基金National Basic Research Program of China(2015CB452705)
文摘A combination of rapid industrialization, economic development and urbanization has caused a series of issues such as resource shortages, ecosystem destruction, environmental pollution and tension between human needs and land conservation. In order to promote balanced development of human, resources, ecosystems, the environment, and the economy and society, it is vital to conceptualize ecological spaces, production spaces and living spaces. Previous studies of ecological-production-living spaces focused mainly on urban and rural areas; few studies have examined mountainous areas. The Taihang Mountains, a key area between the North China Plain and Beijing-Tianjin-Hebei area providing ecological shelter and the safeguarding of crucial water sources, suffer from increasing problems of fragile environment, inappropriate land use and tensions in the human-land relationship. However, studies of the ecological, production, and living spaces in the Taihang Mountains are still lacking. Therefore, this study, based on the concept of ecological-production-living spaces and using data from multiple sources, took the Taihang Mountains as the study area to build a functional land classification system for ecological-production-living spaces. After the classification system was in place, spatial distribution maps for ecological, production and living spaces were delineated. This space mapping not only characterized the present land use situation, but also established a foundation for future land use optimization. Results showed that the area of ecological space was 78,440 km^2, production space 51,861 km^2 and living space 6,646 km^2, accounting for 57.28%, 37.87% and 4.85% of the total area, respectively. Ecological space takes up the most area and is composed mainly of forests and grasslands. Additionally, most of the ecological space is located in higher elevation mountainous areas, and plays an important role in regulating and maintaining ecological security. Production space, mostly farmlands sustaining livelihoods inside and outside the region, is largely situated in lower elevation plains and hilly areas, as well as in low-lying mountainous basins. Living space has the smallest area and is concentrated mainly in regions with relatively flat terrain and convenient transportation for human settlements.
基金supported by National Natural Science Foundation of China(Grant No.11071083)
文摘New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann surfaces.Except inclusions between these generalized spaces it is shown that the capacity Bloch space is a maximal space for them.
基金supported by the National Natural Science Foundation of China (Grant Nos. 4107108, 40771075, 40371044 and 440071037)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Central place theory is one of the two theoretical cornerstones of geography, yet it cannot be connected with other spatial structure models, fails to provide definite time-space parameter conditions, lacks an evolutionary process model, and does not easily enable construction of a complete theoretical system of regional spatial structure. This paper gives an in-depth analysis of the process and mechanism for production and evolution of central places of different grades, and constructs an evolutionary model of the central place hierarchical system. The results of deduction, analysis and simulation show that production and evolution of the central place hierarchical system may be divided into five stages. These stages are the embryonic, formative, improvement, maturation, and advancement stages. Affected by spatial location and centricity, central places have obvious differences in scale and functional structures. There are great differences in the scale of same-grade central places. However, low-grade central places could have larger scales than high-grade central places, and the central places of a central location may form the agglomeration area of central places. Based on the hypothesis condition of an isotropic plain, the research shows that it is possible not only to form proportional functional structures of central places, but also to produce non-proportional scale structures of central places, and thus to complete the transformation from rationalistic deduction of spatial equilibrium mode to an explanation and demonstration of an unbalanced practical model.
基金supported by the National Natural Science Foundation of China(Nos.11401530,11461033,11271330)the Natural Science Foundation of Zhejiang Province(No.LQ13A010018)
文摘In this paper, the authors first give the properties of the convolutions of Orlicz- Lorentz spaces Aφ1,w and Aφ2,w on the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Aφ1,w and Aφ2,w, and get the space of multipliers from the space Aφ1,w to the space Mφ2.w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Aφ,w^p,q.
