Nash Inequalities for Markov Processes in Dimension One

In this paper, we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product, we prove that for these processes, transience implies that the semigroups P(t) decay as ∥P(t)∥_1→∞≥Ct ₋₁. Sufficient conditions for general Markov chains are also obtained. Received November 29, 2000, Revised February 21, 2001, Accepted March 16, 2001     

区域Hardy空间的原子分解和对偶空间

研究D-C chang等人引进的五个区域Hardy空间，刻划这些空间的原子分解和对偶空间，揭示了这些空间的内在联系。     

Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

The authors establish the boundedness of some sublinear operators in weighted Herz spaces on Vilenkin groups under certain weak local hypotheses on the size of these operators at the identity. This class of operators includes most of the important operators in harmonic analysis on Vilenkin groups. The main theorems are best possible under the conditions of the theorems. As applications, the authors establish the Littlewood-Paley function characterization of some Herz spaces and the relations between Herz spaces and Herz-type Hardy spaces.     

Φ-INEQUALITIES AND LAWS OF LARGE NUMBERS OF HARDY MARTINGALETRANSFORMS

In[101,GarlinghasintroducedtheAUMDpropertyofComplexBanachspaceusinginequalityofmartingaletransforms,somefactsshowwhichdiffersfromUMDpropertyofrealBanachspaceintroducedbyBurkholder[6].GarlingalsoprovedthatAUMDpropertyimpliessuperreflexivityandARNP.In[13],XuprovedHMT.isequivalenttoAMT.thatistheBanachspacesforwhicllHardymartingalesconvergeunconditiollallyarethoseforwhichanalyticmartingalesconvergeunconditionally.Hardymartingalesandanalyticmartingalesformaspecialclassofmartingalesforwh…     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.     

齐次群上新Hardy空间的分子特征及其应用

建立了齐次群上伴随于Herz空间和Beurling代数的Hardy空间的分子分解理论．作为其应用．研究了中心强奇异Calderon-Zygmund算子在这些空间上的有界性．     

带Dini核的多线性算子在Herz型Hardy空间上的估计

In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.     

Embedding of analytic function spaces with given mean growth of the derivative

If ? is a positive function defined in [0, 1) and 0 < p < ∞, we consider the space ??(p, ?) which consists of all functions f analytic in the unit disc ?? for which the integral means of the derivative M _p (r, f ′) = 0 < r < 1, satisfy M _p (r, f ′) = O(? (r)), as r → 1. In this paper, for any given p ∈ (0, 1), we characterize the functions ?, among a certain class of weight functions, to be able to embedd ??(p, ?) into classical function spaces. These results complement other previously obtained by the authors for p ≥ 1. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strongly singular convolution operators on the weighted Herz-type Hardy spaces

Let 0<p≤1<q<0, andw ₁ ,w ₂ ∈ A ₁ (Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spacesH K^{α, p} _q(w₁; w₂) to the homogeneous weighted Herz spacesK ^{α, p} _q (w₁; w₂), provided α=n(1−1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spacesH K ^{α, p} _q (w ₁;w ₂) is also investigated. Supported by the National Natural Science Foundation of China