Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces
Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces
复制标题
DOI：
10.1002/mana.202000332
复制
发表时间：
2021-07
影响因子：
1
通讯作者：
Ryota Kawasumi;E. Nakai;Minglei Shi
中科院分区：
文献类型：
--
作者：
Ryota Kawasumi;E. Nakai;Minglei Shi
给出了广义分数积分和极大算子在Orlicz-Morrey和弱Orlicz-Morrey空间上的有界性的充分必要条件。为此，我们证明了Hardy-Littlewood极大算子关于Young函数的弱-弱型模不等式。Orlicz - Morrey空间包含Lp $L^p$空间（1≤p≤∞$1\le p\le \infty$）、Orlicz空间和作为特例的广义Morrey空间。由此，我们得到了这些函数空间的充分必要条件作为推论。
We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces. To do this, we prove the weak–weak type modular inequality of the Hardy–Littlewood maximal operator with respect to the Young function. Orlicz–Morrey spaces contain Lp$L^p$ spaces ( 1≤p≤∞$1\le p\le \infty$ ), Orlicz spaces, and generalized Morrey spaces as special cases. Hence, we get necessary and sufficient conditions on these function spaces as corollaries.