MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Generalization of the Pecaric-Rajic Inequality in a Quasi-Banach Space

In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, and obtain the corresponding upper and lower bounds. As a result, we get some more general inequalities.

A HYBRID FIXED POINT RESULT FOR LIPSCHITZ HOMOMORPHISMS ON QUASI-BANACH ALGEBRAS

We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.

Homomorphisms in Quasi-Banach Algebras Associated with a Pexiderized Cauchy-Jensen Functional Equation

In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.

Weak Hardy-type spaces associated with ball quasi-Banach function spaces I:Decompositions with applications to boundedness of Calderón-Zygmund operators

Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then establish several real-variable characterizations of WH_(X)(R^(n)),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(the mixed-norm Lebesgue space)and X:=(EΦq)t(Rn)(the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasiBanach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable.

Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces

Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.

Generalized Hyers-Ulam Stability of a General Mixed Additive-cubic Functional Equation in Quasi-Banach Spaces

In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation

Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type:Littlewood–Paley Characterizations with Applications to Boundedness of Calderón–Zygmund Operators

Let(X,ρ,μ)be a space of homogeneous type in the sense of Coifman and Weiss,and Y(X)a ball quasi-Banach function space on X,which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space.The authors first introduce the Hardy space H_(Y)(X)associated with Y(X),via the Lusin-area function,and then establish its various equivalent characterizations,respectively,in terms of atoms,molecules,and Littlewood–Paley g-functions and g_(λ)^(*)-functions.As an application,the authors obtain the boundedness of Calderón–Zygmund operators from H_(Y)(X)to Y(X),or to H_(Y)(X)via first establishing a boundedness criterion of linear operators on H_(Y)(X).All these results have a wide range of generality and,particularly,even when they are applied to variable Hardy spaces,the obtained results are also new.The major novelties of this article exist in that,to escape the reverse doubling condition ofμand the triangle inequality ofρ,the authors subtly use the wavelet reproducing formula,originally establish an admissible molecular characterization of H_(Y)(X),and fully apply the geometrical properties of X expressed by dyadic reference points or dyadic cubes.

Isometries on the Quasi-Banach Spaces L^p (0 < p <1)

We study the extension of isometries between the unit spheres of quasi-Banach spaces Lp for 0〈p〈1. We give some sufficient conditions such that an isometric mapping from the the unit sphere of Lp（μ） into that of another LP（ν） can be extended to be a linear isometry defined on the whole space.

Complex interpolation and Calderon product of quasi-Banach spaces

We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderon product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.

Banach代数中两个元素之和与积的广义Drazin逆

令a,b为具有单位元1的Banach代数A中两个广义Drazin逆的元素,a^(d)为a的广义Drazin逆.利用Banach代数中的幂等系统考虑两个元素之和与积的广义Drazin逆,在ab 2=bab,b^(π)ba^(2)=bπaba,a^(d)b 2=ba^(d)b等条件下给出a,b之和与积的广义Drazin逆的表达式.

Banach空间中一类分裂等式可行问题的强收敛定理

为了在Banach空间中得到分裂等式公共不动点问题的强收敛性,在适当的条件下构造了一种新的迭代算法,并在更具一般性的条件下证明了由该算法生成的序列强收敛于分裂等式不动点问题的一个解.最后,根据所得结论进一步得到了分裂等式均衡问题与极大单调算子零点问题的强收敛性定理.

相关于增长函数的非交换Orlicz空间的一致凸性

相关于增长函数的非交换Orlicz空间是拟Banach空间,研究了这类拟Banach空间的一致凸性.首先,得到了这类空间上的模和Luxemburg拟范数的控制关系.其次,给出了这类空间的一致凸性,并且估计了凸性的模.最后,给出了满足假设的具体空间的例子.

一类新型广义逆及其应用

引进了一类Banach代数的新型广义逆并研究了它的等价特征,在正交条件和交换条件下讨论了它们的加法不变性.作为应用,探究了Banach空间上算子矩阵的Mosic-Abyzov可逆性,获得了算子矩阵拟Nil-clean性刻画.

拟Banach空间上的凸性模与特殊鞅不等式

在拟Banach空间上引入了TC凸性模,它是一致凸性模的推广,并证明了重赋拟范定理,在此基础上研究了取值于拟Banach空间的一类特殊鞅不等式与该空间的q一致TC可凸性的关系,从而用特殊鞅不等式刻画了空间的q一致TC可凸性.

复拟Banach空间的PL一致光滑性及其鞅刻划

本文引进了复空间的ＰＬ一致光滑性与复对称鞅，证明了等价赋范定理，得到了一系列关于ＰＬ一致光滑空间的复对称鞅不等式·并应用复对称鞅的大数定律给出了值空间的ＰＬ一致光滑性的刻划·

渐近拟非扩张映射的三步迭代序列的收敛定理

证明了在实Banach空间中当T是渐近似非扩张自映射时,三步迭代序列收敛到T的不动点.

2-赋范空间和拟Banach空间中的华罗庚不等式

华罗庚在1965年发现的华罗庚不等式在数论中有着重要的应用,它得到了很多的推广。将华罗庚不等式推广到严格凸的2-赋范空间和拟Banach空间。

复拟Banach空间的解析q一致凸性与Hardy鞅的原子分解

用Hardy鞅的原子分解刻画了复拟Banach空间的解析q一致凸性,并用原子分解证明了两个Hardy鞅空间的嵌入关系.

Banach代数中广义Drazin逆的相关结果

令a,b均为Banach代数中广义Drazin可逆的元素,a^d为a的广义Drazin逆,a^π=1-aa^d.用Banach代数中的幂等元给出元素a,b在ab^π=a,b^πba^π=b^πb,b^πa^πa^2b=b^πa^πaba,b^πa^πb^2a=b^πa^πbab等条件下a+b广义Drazin逆的表达式.