A remark on the (H1, L1) boundedness
A remark on the (H1, L1) boundedness
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DOI：
10.5036/bfsiu1968.25.19
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
K. Yabuta
中科院分区：
文献类型：
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作者：
K. Yabuta
对所有原子f∈ H_1（Rn），其中D（Rn）是Rn上具有紧支集的无穷可微函数空间，D ′（Rn）是它的对偶，H_1（Rn）是E. M. Stein和G.韦斯。这里，f被称为原子，如果f（x）dx=0，f的支撑包含在立方体Q中，并且其中|Q| Q的勒贝格测度。一般来说，人们不能从（*）得出（2*）的结论（我从A. Miyachi.）为了得到（2*），将（3*）作为适当原子分解的调和分布就足够了。例如，（3*）本质上由Y表示。Meyer的奇异积分算子（[1]，p.234）.因此，给出（2*）的以下充分条件并非毫无意义。提案1.设T是从D 0到Lr（Rn）的线性算子，使得
for all atoms f∈H1(Rn), where D(Rn) is the space of all infinitely differentiable functions on Rn with compact support, D'(Rn)is its dual, and H1(Rn) is the Hardy space introduced by E.M. Stein and G. Weiss. Here, f is said to be an atom if ∫f(x)dx=0, the support of f is contained in a cube Q, and where |Q| means the Lebesgue measure of Q. In general, one cannot conclude from (*) that (2*) (I have learned a proof of this fact from A. Miyachi.) To get (2*), it suffices that (3*) as tempered distributions for an appropriate atomic decomposition For example, (3*) is essentially noted by Y. Meyer for singular integral operators ([1], p. 234). So, it will be not meaningless to give the following sufficient condition for (2*). PROPOSITION 1. Let and Suppose T is a linear operator from D0 toLr(Rn) such that