Endpoint estimates for multilinear fractional integrals with non-doubling measures

Under the assumption that μ is a non-doubling measure on Rdwhich only satisfies the polynomial growth condition,the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces,weak-Morrey spaces and Lipschitz spaces associated with μ,which,in the case when μ is the d-dimensional Lebesgue measure,also improve the known results.     

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calder′on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 p +∞if and only if b∈BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσbe the operators that its symbol is S01,δwith 0≤δ 1, if b∈LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L∞(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L∞(Rn) into BMO(Rn), then, b∈LMO_(loc).     

Commutators of parabolic singular integrals on the generalized Morrey spaces

Let[b,T]be the commutator of parabolic singular integral T.In this paper,the authors prove that the boundedness of[b,T]on the generalized Morrey spaces implies b∈BM O(Rn,ρ).The results in this paper improve and extend the Komori and Mizuhara’s results.     

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

Modifying the method of Ansari,we give some criteria for hypercyclicity of quasi-Mazur spaces.They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces.For some special locally convex spaces,for example,Ko¨the(LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces,we investigate their hypercyclicity.As we see,bounded biorthogonal systems play an important role in the construction of Ansari.Moreover,we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets,which are useful in judging the existence of bounded biorthogonal systems.     

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.     

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0≤α相似文献   

VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid-ered. Results on orthogonality of the ran...     

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.     

ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN C~n

Let μ be a normal function on [0, 1). The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 0.     

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

In this paper, we obtain some new necessary and suffcient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.     

The Relations between Discrete Frames and Continuous Frames with Respect to （N, μ）

The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.     

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article,we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.     

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.     

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.     

AN IMPROVED HARDY＇S INEQUALITY

In this paper we shall extend Hardy’s inequality associated with Fourier trans-form to the strip n(2?p)≤σ相似文献   

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.     

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lpspaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H∞functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.     

BOUND STATES FOR A STATIONARY NONLINEAR SCHRODINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3△

We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0     

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...     

Boundedness for a Class of Generalized Commutators on λ-Central Morrey Space

Let 0 ≤α n,Ω be a rough kernel,and let A have derivatives of order m 1 in CBBMOq,μ2 with m ≥ 2.We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type,and obtain the boundedness of TΩA,α from the central Morrey spaces Ep,μ1 to Er,λ for λ = μ1 + μ2 + α/n and 1/r = 1/p + 1/q α/n.