摘要：

We study the endpoint regularity of the one-dimensional discrete multisublinear fractional maximal operators, both in the centered and uncentered versions. Some new variation inequalities will be proved for the above operators acting on the vector-valued function \(\mathbf {f}=(f_1, \ldots ,f_m)\) with each \(f_j\) belonging to \(\mathrm{BV}({\mathbb {Z}})\) or \(\ell ^1({\mathbb {Z}})\), where \(\mathrm{BV}({\mathbb {Z}})\) denotes the set of functions of bounded variation defined on \({\mathbb {Z}}\). In addition, it was also shown that the above operators are bounded and continuous from \(\ell ^1({\mathbb {Z}})\times \cdots \times \ell ^1({\mathbb {Z}})\) to \(\mathrm{BV}({\mathbb {Z}})\). The above results represent significant and natural extensions of what was known previously.

作者：

Zhang Xiao

链接：

https://link.springer.com/article/10.1007/s00025-021-01387-5