Multilinear estimates and fractional integration
Multilinear estimates and fractional integration
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DOI：
10.4310/mrl.1999.v6.n1.a1
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发表时间：
1999
影响因子：
1
通讯作者：
C. Kenig;E. Stein
中科院分区：
文献类型：
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作者：
C. Kenig;E. Stein
并且PI还受到要求R > 23（而不是R > 12）的限制。条件r > 2 3是证明中使用的方法的结果，并且可能不是必要的;这些方法是复杂的，并且在关键点依赖于L估计。返回到分数积分情况K（y）=| y| −n+α，我们将在下面通过非常基本的考虑证明I映射L1 × Lp 2 → L对于整个范围：即，当1 < pi ≤ ∞时，i = 1，2，
and the pi are additionally restricted by the requirement r > 23 (instead of r > 12 ). The condition r > 2 3 is a consequence of the methods used in their proof, and may not be necessary; these methods are intricate and at a crucial point rely on L estimates. Returning to the fractional integration case K(y) = |y|−n+α, we shall prove below — by very elementary considerations — that I maps L1 ×Lp2 → L for the full range: i.e., when 1 < pi ≤ ∞, i = 1, 2, and