Four Lectures on Real H^P Spaces

Weighted Boundedness of Multilinear Operators for the Extreme Cases

“…which is the maximal Bochner-Riesz operator (see [12][14] [15]). The variant of B A δ, * is defined by…”

“…Case 1. 0 < t ≤ d. In this case, notice that (see [14]) Case 2. t > d. In this case, we choose δ 0 such that (n − 1)/2 < δ 0 < min(δ, (n + 1)/2), notice that (see [15]) These yield the desired results. A same argument as in the proof of Theorem 1 will give the proof of (ii), (iii), (iv) and (v), we omit the details.…”

Intrinsic Square Function Characterizations of Variable Weak Hardy Spaces

“…It is well known that, when studying the boundedness of some operators in the critical case, the weak Hardy space WH p (R n ) with p ∈ (0, 1] is a good substitute of the Hardy space H p (R n ) (see [5,6,13,16,23,28,31,40]). Moreover, the space WH p (R n ) was proved as the intermediate space in the real interpolation between the Hardy space H p (R n ) and the space L ∞ (R n ) (see [1,14,25,46]). Motivated by these, Yan et al [40] first introduced the variable weak Hardy spaces WH p(•) (R n ) via the radial grand maximal function and characterized these spaces by means of maximal functions, atoms, molecules and Littlewood-Paley functions.…”

The equivalence of a class of generalized Bochner-Riesz multipliers and its applications

“…对于 0 < p 1 的情形, 文献 [2,3] 分别研究了乘子 T m 在 H p 上的有界性问题, 得到下面的定理 C. 此外, 陆善镇 [4] 给出了判断函数 m 是否为 H p (R n ) 乘子的另外一个结果, 表述为定理 D.…”

“…事实上, 定理 D 给出了函数 m 成为 Hardy 空间 H p (R n ) 上的乘子的充分条件. 需要指出的是, 引 理的假设条件可减弱至更为一般的 Hörmander 条件, 证明以及相关评注可参见文献 [4] 和此专著中的 相关文献. [5] .…”