Fuzzy S-Regular Spaces and S-Almost Regular Spaces

ＦｕｚｚｙＳＲｅｇｕｌａｒＳｐａｃｅｓａｎｄＳＡｌｍｏｓｔＲｅｇｕｌａｒＳｐａｃｅｓＦａｎｇＪｉｎｍｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＯｃｅａｎＵｎｉｖｅｒｓｉｔｙｏｆＱｉｎｇｄａｏ，Ｑｉｎｇｄａｏ，２６６０...     

Teichmüller Spaces and Function Spaces

ＴｅｉｃｈｍüｌｅｒＳｐａｃｅｓａｎｄＦｕｎｃｔｉｏｎＳｐａｃｅｓＧｕｏＨｕｉ（郭辉）（ＳｃｈｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＬｉＺｈｏｎｇＲ...     

Characterizations of K-smooth Spaces and K-strongly Smooth Spaces

Some necessary and sufficient conditions for a Banach space to be K-smooth or Kstrongly smooth are obtained.     

Variable Besov-type Spaces

In this paper we introduce Besov-type spaces with variable smoothness and integrability.We show that these spaces are characterized by the φ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces.Moreover the Sobolev embeddings for these function spaces are obtained.     

Toric Rigid Spaces

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.     

On P-sober Spaces

In this paper,we focus on p-sober spaces and prove that(1) the To space X is p-sober if and only if the Smyth power space of X is p-sober;(2) the space X has a p-sober dcpo model if and only if X is T₁ and p-sober;(3) every non-p-sober T₀ space does not have a p-sobrification;(4) the T₀ space X is sober if and only if X is p-sober and PD.     

γ-Compact Spaces

Let X be a topological space, denote iA and cA the interior and the closure of A ⊂ X, respectively, and let γ = c o i, or = i o c, or = i o c o i, or = c o i o c. A set A ⊂ X is said to be γ-open [5] iff A ⊂ γ(A). The space X is γ-compact iff each cover of X composed of γ-open sets admits a finite subcover. The purpose of the paper is to investigate some questions concerning γ-compact and related spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Function Spaces on τ-Corson Compacta and Tightness of Polyadic Spaces

We apply the general theory of -Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness . In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.     

Regular Spaces and Hyper-spaces

We are concerned with the construction of regular spaces and hyper-spaces,and the characterization of continuous linear operators in such spaces.     

L~P-orthogonality in Banach Spaces

The notion of L~P-orthogonality was posed by F. Sullivan [1], but it hadnever been studied. The purpose of this paper is to give some results concerningthe L~P-orthogonality in Banach spaces.     

Very Convex Banach Spaces

ＶｅｒｙＣｏｎｖｅｘＢａｎａｃｈＳｐａｃｅｓＴｅｇｕｓｉ（特古斯）Ｓｕｙａｌａｔｕ（苏雅拉图）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｎｅｒＭｏｎｇｏｌｉａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈｕｈｈｏｔ，０１００２２）ＬｉＹｏｎｇｊｉｎ...     

Embedding of Möbius Invariant Function Spaces into Tent Spaces

On the unit disk we introduce a new class of tent spaces \(T^q_{s,t}(\mu )\) for any positive Borel measure \(\mu \), consider a class of Möbius invariant spaces \(Z_p\) of analytic functions, and show that \(Z_p\) is contained in \(T^1_{p,1}\) if and only if \(\mu \) is a p-Carleson measure. This could be considered a continuation or variation of the work initiated by Xiao (Adv Math 217:2075–2088, 2008).     

Amarts on Riesz Spaces

The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson （Discrete time stochastic processes on Riesz spaces, Indag. Math.,15（2004）, 435-451）. Here we extend the definition of an asymptotic martingale （amart） to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Hardy Spaces, Regularized BMO Spaces and the Boundedness of Calderón–Zygmund Operators on Non-homogeneous Spaces

One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r ⁿ for some n>0. The aim of this paper is to study the boundedness of Calderón–Zygmund singular integral operators T on various function spaces on (X,μ) such as the Hardy spaces, the L ^p spaces, and the regularized BMO spaces. This article thus extends the work of X. Tolsa (Math. Ann. 319:89–149, 2011) on the non-homogeneous space (? ⁿ ,μ) to the setting of a general non-homogeneous space (X,μ). Our framework of the non-homogeneous space (X,μ) is similar to that of Hytönen (2011) and we are able to obtain quite a few properties similar to those of Calderón–Zygmund operators on doubling spaces such as the weak type (1,1) estimate, boundedness from Hardy space into L ¹, boundedness from L ^∞ into the regularized BMO, and an interpolation theorem. Furthermore, we prove that the dual space of the Hardy space is the regularized BMO space, obtain a Calderón–Zygmund decomposition on the non-homogeneous space (X,μ), and use this decomposition to show the boundedness of the maximal operators in the form of a Cotlar inequality as well as the boundedness of commutators of Calderón–Zygmund operators and BMO functions.     

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

§１．　Ｄｅｆｉｎｉｔｉｏｎｓ，ＬｅｍｍａｓａｎｄＴｈｅｏｒｅｍＤｅｆｉｎｉｔｉｏｎ１［１］　Ｌｅｔ（Ｘ，ｙ·ｙ）ｂｅａｒｅａｌｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅｏｆｄｅｍｅｎｓｉｏｎｇｒｅａｔｅｒｔｈａｎ１，ｗｅｄｅｆｉｎｅａｎｇｌｅｓＡｍ，ｎ（ｘ，ｙ）ｂｅｔｗｅｅｎｎｏｎｚｅｒｏｖｅｃｔｏｒｓｘａｎｄｙｉｎＸｂｙＡｍ，ｎ（ｘ，ｙ）＝ｃｏｓ－１ｎｙｘｙｘｙ＋ｙｙｙｙｙ２－ｍｙｘｙｘｙ－ｙｙｙｙｙ２＋２（ｍ－ｎ）２（ｍ＋ｎ），ｈｅｒｅｍａｎｄｎａｒｅｔｗｏｎｏｎ－ｎｅｇｅｎｔｉｖｅｉｎｔｅ－ｇｅ…     

Geometric Properties of Symmetric Spaces with Applications to Orlicz–Lorentz Spaces

We deal with the basic convexity properties –rotundity, and uniform, local uniform and full rotundity –- for symmetric spaces. A characterization of Orlicz–Lorentz spaces with the Kadec–Klee property for pointwise convergence is given. These results are applied to obtain criteria of convexity properties for Orlicz–Lorentz sequence spaces, and some new proofs of the sufficiency part of criteria for rotundity and uniform rotundity for Orlicz–Lorentz function spaces.     

On Weighted α-Besov Spaces and α-Bloch Spaces of Quaternion-Valued Functions

In this paper, we give the definitions of weighted α-Besov-type spaces and α-Bloch spaces of quaternion-valued functions, then we obtain characterizations of these quaternion α-Bloch spaces by quaternion α-Besov-type spaces. Relations between Q _p norms and weighted α-Besov norms are also considered. The role of ρ?^α sequences in securing non-Bloch functions is highlighted in quaternion sense.     

Characterization of Day–James Spaces and Generalized Day–James Spaces

In this paper, we introduce the definition of generalized Day–James space on R~n(n ≥2) and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary condition for Day–James space, which reappeared Day's construction for any two-dimensional normed space to make Birkhoff orthogonality symmetry.     

Some Characterizations of Lipschitz Spaces via Commutators on Generalized Orlicz–Morrey Spaces

In this paper, we give some new characterizations of the Lipschitz spaces via the boundedness of commutators associated with the fractional maximal operator, Riesz potential and Calderón–Zygmund operator on generalized Orlicz–Morrey spaces.