RIESZ TRANSFORM CHARACTERIZATIONS OF MUSIELAK-ORLICZ-HARDY SPACES
RIESZ TRANSFORM CHARACTERIZATIONS OF MUSIELAK-ORLICZ-HARDY SPACES
复制标题
Musielak-Orlicz-Hardy 空间的 Riesz 变换表征
DOI：
10.1090/tran/6556
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发表时间：
2016-10-01
影响因子：
1.3
通讯作者：
Yang, Sibei
中科院分区：
文献类型：
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作者：
Cao, Jun;Chang, Der-Chen;Yang, Sibei
设偏导数为aMusielak-Orlicz函数，满足对任意（x, t）是r - nx（0,∞）的元素，（中心点，t）属于Muckenhoupt权类A(∞)（R-n)，其临界权指数q（phi）是[1，∞）的元素，且（x，中心点）是0 < i(phi) n-1/n+ m1的Orlicz函数。此外，作者还分别利用齐次调和多项式定义的高阶Riesz变换和奇阶Riesz变换建立了H φ (R-n)的Riesz变换表征。即使当φ(x, t): = tw (x)为所有x r n和t的一个元素是一个元素(0,8),这些结果也扩大范围已知重量的黎兹古典加权哈代空间的表征H-w (1) (r n)通过r . l . Wheeden w是(1)的一个元素(r n) w(∞)的一个元素(r n)大幅范围q (w)是一个元素(1,n / n - 1), q (w)表示重量的关键指数w。
Let partial derivative be aMusielak-Orlicz function satisfying that, for any (x, t) is an element of R-n x (0, infinity), phi(center dot, t) belongs to the Muckenhoupt weight class A(infinity)(R-n) with the critical weight exponent q(phi) is an element of[1, infinity) and phi(x, center dot) is an Orlicz function with0 < i(phi) n-1/n+m 1. Moreover, the authors also establish the Riesz transform characterizations of H phi(R-n), respectively, by means of the higher order Riesz transforms defined via the homogenous harmonic polynomials or the odd order Riesz transforms. Even if when phi(x, t) := tw(x) for all x is an element of R-n and t is an element of [0,8), these results also widen the range of weights in the known Riesz characterization of the classical weighted Hardy space H-w(1) (R-n) obtained by R. L. Wheeden from w is an element of A(1)(R-n) into w is an element of A(infinity)(R-n) with the sharp range q(w) is an element of[1, n/n-1), where q(w) denotes the critical index of the weight w.