In this paper, Orlicz space endowed with Orlicz norm are discussed. We discovered that P-convexity, O-convextiy, Q-convexity, superreflexirity and teflexivity are equivalent.
In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coef...In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coefficients of the functions in Bers-Orlicz spaces are given.展开更多
In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems includ...In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.展开更多
Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we ...Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).展开更多
Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces.This complements earlier work[26]where we made a strong case for the assertion that statistical physics of regular ...Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces.This complements earlier work[26]where we made a strong case for the assertion that statistical physics of regular systems should properly be based on the pair of Orlicz spaces(Lcosh-1,L log(L+1)),since this framework gives a better description of regular observables,and also allows for a well-defined entropy function.In the present paper we"complete"the picture by addressing the issue of the dynamics of such a system,as described by a Markov semigroup corresponding to some Dirichlet form(see[4,13,14]).Specifically,we show that even in the most general non-commutative contexts,completely positive Markov maps satisfying a natural Det ailed Balance condition canonically admit an action on a large class of quantum Orlicz spaces.This is achieved by the development of a new interpolation strategy for extending the action of such maps to the appropriate intermediate spaces of the pair(L∞,L1).As a consequence,we obtain that completely positive quantum Markov dynamics naturally extends to the context proposed in[26].展开更多
Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredho...Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators.展开更多
The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the...The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the completely continuous operator in the space sunder consideration. In this paper, we consider the equations mentioned above in Orlicz spaces L_M(Γ). It is proved that the Nether theorem and the index formula are hold true in the case of reflexive Orlicz spaces.展开更多
Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced,...Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].展开更多
Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp...Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.展开更多
In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduce...In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.展开更多
We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequen...We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.展开更多
In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
文摘In this paper, Orlicz space endowed with Orlicz norm are discussed. We discovered that P-convexity, O-convextiy, Q-convexity, superreflexirity and teflexivity are equivalent.
文摘In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coefficients of the functions in Bers-Orlicz spaces are given.
基金Supported by Hubei Research Center for Financial Development and Financial Security(2008D029)
文摘In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.
基金Supported by the National Natural Science Foundation of China (Grant No.11726622)Scientific Research Fund of Young Teachers in Longqiao College (Grant No. LQKJ2020-01)。
文摘Let φ be a generalized Orlicz function satisfying(A0),(A1),(A2),(aInc)and(aDec). We prove that the mapping f■f^#:=supB|1/B|∫B|f(x)-fp|dx is continuous on L^φ(·)(R^n) by extrapolation. Based on this result we generalize Korn's inequality to the setting of generalized Orlicz spaces, i.e., ‖■f‖Lφ(·)(Ω)■‖Df‖Lφ(·)(Ω). Using the Calderón–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu = f has a solution u ∈(W^1φ(·)(Ω)0)^n such that ‖■f‖Lφ(·)(Ω)■‖f‖Lφ(Ω).
基金supported by the National Research Foundation(IPRR Grant 96128).
文摘Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces.This complements earlier work[26]where we made a strong case for the assertion that statistical physics of regular systems should properly be based on the pair of Orlicz spaces(Lcosh-1,L log(L+1)),since this framework gives a better description of regular observables,and also allows for a well-defined entropy function.In the present paper we"complete"the picture by addressing the issue of the dynamics of such a system,as described by a Markov semigroup corresponding to some Dirichlet form(see[4,13,14]).Specifically,we show that even in the most general non-commutative contexts,completely positive Markov maps satisfying a natural Det ailed Balance condition canonically admit an action on a large class of quantum Orlicz spaces.This is achieved by the development of a new interpolation strategy for extending the action of such maps to the appropriate intermediate spaces of the pair(L∞,L1).As a consequence,we obtain that completely positive quantum Markov dynamics naturally extends to the context proposed in[26].
文摘Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators.
文摘The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the completely continuous operator in the space sunder consideration. In this paper, we consider the equations mentioned above in Orlicz spaces L_M(Γ). It is proved that the Nether theorem and the index formula are hold true in the case of reflexive Orlicz spaces.
文摘Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].
文摘Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.
基金supported by National Natural Science Foundation of China(Grant No.11201354)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(Y201321)National Natural Science Foundation of Pre-Research Item(2011XG005)
文摘In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.
基金supported by the National Natural Science Foundation of China(11726622)the Natural Science Foundation Projection of Chongqing,China(cstc2021jcyj-msxmX0705).
文摘We introduce a class of generalized Orlicz-type Auscher-Mourgoglou slice space,which is a special case of the Wiener amalgam.We prove versions of the Rubio de Francia extrapolation theorem in this space.As a consequence,we obtain the boundedness results for several classical operators,such as the Calderón-Zygmund operator,the Marcinkiewicz integrals,the Bochner-Riesz means and the Riesz potential,as well as variational inequalities for differential operators and singular integrals.As an application,we obtain global regularity estimates for solutions of non-divergence elliptic equations on generalized Orlicz-type slice spaces if the coefficient matrix is symmetric,uniformly elliptic and has a small(δ,R)-BMO norm for some positive numbers δ and R.
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
文摘In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.
