COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS

Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.

Boundedness of Fractional Maximal Operators on Some of Homogeneous Groups

Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.

MAXIMAL CHARACTERIZATIONS OF HERZ TYPE HARDY SPACES ON HOMOGENEOUS GROUPS

In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P（G） and HKq^α,P（G）, where 1 〈 q 〈 ∞, Q（1 - 1/q） ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.

New Hardy Spaces Associated with Herz Spaces and Beurling Algebras on Homogeneous Groups

The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderon-Zygmund operators on these Hardy spaces are studied.

Some Estimates for Convolution Operators with Kernels of Type (l, r) on Homogeneous Groups

Some estimates for the convolution operators with kernels of type （l, r） on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established.

齐次群上多线性奇异积分算子的有界性(英文)

Let G be a homogeneous group. In this paper, the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G. As its special case, the corresponding result of multilinear Calderon-Zygmund operators can be obtained.

An Exploration of Teaching Class of Mixed Ability

There has been a long time of debate between the two teaching approaches of homogenous grouping and heterogeneous grouping.Here in the essay,we explored both of the two teaching approaches in Yunnan Province of China whereas the puzzle lies in the question of which method can achieve a relatively-better result in English classes of Yunnan.Some possible solutions are promoted based on the data and analysis collected from a survey.