Weighted HARDY Spaces
Weighted HARDY Spaces
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DOI：
10.1002/mana.19811030106
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发表时间：
1981
影响因子：
1
通讯作者：
Bui Huy Qui
中科院分区：
文献类型：
--
作者：
Bui Huy Qui
本文的主要目的是研究GOLDBERC [113]最近考虑的局部哈代空间hp的加权形式hz，其中权w假定满足MUCKENHOUPT的条件（A，）.在第1节给出了关于带域上权函数和调和函数的初步结果之后，我们在第2和第3节中采用GUNDY-WHEEDEN [12]和WHEEDEN [22]的论证，研究了hP的一般性质。我们还打算获得尽可能接近非加权情况的结果。为了实现这一目标，在本文的后半部分，我们将自己限制在类A中的权重。通过对权重w的这种限制，在p= 1的情况下获得了令人满意的结果，包括hf的表征，根据n个RIESZ变换I ′ ~…，r，对于H1和h：的Füberman-Stein特征（[8]）和原子分解（[4]，[6]，[13]）。这些结果分别在第3、4和5节中给出。作为结果，H：和h：之间的联系，以及作为空间bmo的hi的对偶的表示被导出。作者感谢与H教授的有益通信。TRIEBEL mtl R. L.在准备本文期间。
The main purpose of this paper is to study the weighted version hz of the local HARDY space hp considered recently by GOLDBERC [113, where the weight w is assumed to satisfy the condition (A,) of MUCKENHOUPT. After giving preliminary results concerning weight functions and harmonic functions on the strip domain in Section 1, we investigate the general properties of hP, by adopting the arguments of GUNDY-WHEEDEN [12] and WHEEDEN [22] in Sections 2 and 3. It is also our intention to obtain results as close as possible to the non-weighted case. To achieve this aim, in the later part of the paper we restrict ourselves to weights in the class A,. IKth this restriction on the weight w, satisfactory results are obtained in the case p= 1 including the characterization of hf, in terms of the n RIESZ transforms I'~...., r,, the FEFFERMAN-STEIN characterization ([8]) and the atomic decomposition ([4],[6],[13]) for both Hi and h:. These results are given in Sections 3, 4 and 5, respectively. As a consequence, the connection between H: and h:, and the representation of the dual of hi as the space bmo, are derived. The author acknowledges helpful correspondences with Professor H. TRIEBEL mtl Professor R. L. WHEEDEN during the preparation of this paper.