In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q ...In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.展开更多
In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/...Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n for n/2(n+1)<s≤n/2.展开更多
In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operat...In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.展开更多
Based on the idea of hypothetical 4-dimensial substance with an inverse population of energy levels, a model of accelerated expansion of the Universe has been developed, which describes Hubble diagrams with great accu...Based on the idea of hypothetical 4-dimensial substance with an inverse population of energy levels, a model of accelerated expansion of the Universe has been developed, which describes Hubble diagrams with great accuracy for type Ia supernovae, quasars and gamma-ray burst sources at the Hubble parameter value of 67.7 km/s/Mpc, coinciding with the value obtained from analysis of inhomogeneities of relic radiation. Calculations at the Hubble parameter value of 73.5 km/s/Mpc, obtained using the ΛCDM model based on the analysis of data on type Ia supernovae and cepheids, differ markedly from the observed data. An explanation of the two values of the Hubble constant is proposed. It is shown that in this model, the magnitude of 13.8 billion years characterizes not the age of the Universe, but the time of propagation of light from those galaxes whose acceleration of removal has a minimal value. Based on the recently discovered curvature of the Universe, estimates are given of the lower limits of its size and lifetime, which turned out to be at least 270 billon years. The probability of transition from the excited state to the underlying energy levels of a hypothetical 4-dimensial substance, as well as the low of increasing energy density as a result of transitions to the underlying levels of this substance, is determined.展开更多
基金The NSF (Q2008A01) of Shandong,Chinathe NSF (10871024) of China
文摘In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.
基金Supported by the National Natural Science Foundation of China(11201003)Supported by the Education Committee of Anhui Province(KJ2012A133)
文摘In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
基金Li Dan and Li Junfeng were supported by NSFC-DFG(11761131002)NSFC(12071052)Xiao Jie was supported by NSERC of Canada(202979463102000).
文摘Given n≥2 and α≥1/2,we obtained an improved upbound of Hausdorff's dimension of the fractional Schrodinger operator;that is,supf∈H^(s)(R^(n)) dim_(H){x∈R^(n):limt→0 e^(it)(-△)^(α) f(x)≠f(x)}≤n+1-2(n+1)s/n for n/2(n+1)<s≤n/2.
文摘In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.
文摘Based on the idea of hypothetical 4-dimensial substance with an inverse population of energy levels, a model of accelerated expansion of the Universe has been developed, which describes Hubble diagrams with great accuracy for type Ia supernovae, quasars and gamma-ray burst sources at the Hubble parameter value of 67.7 km/s/Mpc, coinciding with the value obtained from analysis of inhomogeneities of relic radiation. Calculations at the Hubble parameter value of 73.5 km/s/Mpc, obtained using the ΛCDM model based on the analysis of data on type Ia supernovae and cepheids, differ markedly from the observed data. An explanation of the two values of the Hubble constant is proposed. It is shown that in this model, the magnitude of 13.8 billion years characterizes not the age of the Universe, but the time of propagation of light from those galaxes whose acceleration of removal has a minimal value. Based on the recently discovered curvature of the Universe, estimates are given of the lower limits of its size and lifetime, which turned out to be at least 270 billon years. The probability of transition from the excited state to the underlying energy levels of a hypothetical 4-dimensial substance, as well as the low of increasing energy density as a result of transitions to the underlying levels of this substance, is determined.
