摘要：

We prove that the local multilinear fractional maximal operator is bounded frhich was previously unknown for thIn addition, we introduce and investigate the Sobolev regularity properties of the local multilinear strong maximal operator, as well as its fractional variant. Several new pointwise estimates for the weak gradients of the above maximal functions will be established)${�}_{�}\in (1,\infty )$. As applications, we obtain certain boundedness for the above operators in the first-order Sobolev spaces and the Sobolev spaces with zero boundary values.

作者：

Liu Feng, Zhang Xiao

链接：

https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-52/issue-5/Regularity-of-local-multilinear-fractional-maximal-and-strong-maximal-operators/10.1216/rmj.2022.52.1887.short