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
Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weight...Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.展开更多
This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists ...This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients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
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.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
The Lipschitz classes Lip（a,M） ,0 〈 a 〈 1 are defined for Orlicz space generated by the Young function M, and the degree of approximation by matrix transforms of f E Lip（or,M） is estimated by n-a.
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
In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
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
In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches ...In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.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
For given data,an interpotant is sought,so that a cerlaint convcx functional de fined bv a Young's function in the corresponding Orlicz space is minuimized.The feedciainmore general kind of spaces can be used for ...For given data,an interpotant is sought,so that a cerlaint convcx functional de fined bv a Young's function in the corresponding Orlicz space is minuimized.The feedciainmore general kind of spaces can be used for selecting the interpolunts in an udequare class of functiois.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
In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical correspo...In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result.展开更多
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.
文摘Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.
基金Supported by Inner Mongolia Natural Science Foundations of China (200408020108).
文摘This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients
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 Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
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).
文摘The Lipschitz classes Lip（a,M） ,0 〈 a 〈 1 are defined for Orlicz space generated by the Young function M, and the degree of approximation by matrix transforms of f E Lip（or,M） is estimated by n-a.
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In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
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.
基金This research is suported by National Science foundation Grant.
文摘In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.
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.
基金Both authors were partically supported by DGICYTPS90/0120
文摘For given data,an interpotant is sought,so that a cerlaint convcx functional de fined bv a Young's function in the corresponding Orlicz space is minuimized.The feedciainmore general kind of spaces can be used for selecting the interpolunts in an udequare class of functiois.
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In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result.
