Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a varie...Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a variety of chemical families,such as hydrogen-bonded organic frameworks,porous organic salts,porous organic cages,C-H···πmicroporous crystals,supramolecular organic frameworks,π-organic frameworks,halogen-bonded organic framework,and intrinsically porous molecular materials.In some porous materials such as zeolites and metal organic frameworks,the integration of multiscale has been adopted to build materials with multifunctionality and optimized properties.Therefore,considering the significant role of hierarchy in porous materials and the growing importance of POMMs in the realm of synthetic porous materials,we consider it appropriate to dedicate for the first time a critical review covering both topics.Herein,we will provide a summary of literature examples showcasing hierarchical POMMs,with a focus on their main synthetic approaches,applications,and the advantages brought forth by introducing hierarchy.展开更多
Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [...Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.展开更多
基金the MICINN (Spain)(Projects PID2019-104778GB-I00, PID2020-115100GB-I00Excellence Unit “Maria de Maeztu” CEX2019-000919-M)+5 种基金the Royal Society of Chemistryfunded by Generalitat Valenciana(PROMETEU/2021/054 and SEJI/2020/034)the “Ramón y Cajal” program (RYC2019-027940-I)the Royal Society (RGSR1221390)Royal Society of Chemistry (R21-5119312833) for the funding.
文摘Porous organic molecular materials(POMMs)are an emergent class of molecular-based materials characterized by the formation of extended porous frameworks,mainly held by non-covalent interactions.POMMs represent a variety of chemical families,such as hydrogen-bonded organic frameworks,porous organic salts,porous organic cages,C-H···πmicroporous crystals,supramolecular organic frameworks,π-organic frameworks,halogen-bonded organic framework,and intrinsically porous molecular materials.In some porous materials such as zeolites and metal organic frameworks,the integration of multiscale has been adopted to build materials with multifunctionality and optimized properties.Therefore,considering the significant role of hierarchy in porous materials and the growing importance of POMMs in the realm of synthetic porous materials,we consider it appropriate to dedicate for the first time a critical review covering both topics.Herein,we will provide a summary of literature examples showcasing hierarchical POMMs,with a focus on their main synthetic approaches,applications,and the advantages brought forth by introducing hierarchy.
文摘Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.
