摘要：

In this paper, we prove that the local multilinear fractional maximal operator is bounded from L1(Ω) × · · · × Lm(Ω) to W (Ω) when 1 < p1, . . . , pm < ∞ and 1/q = 1/p1 + · · ·+ 1/pm with 1 ≤ q <∞, which was previously unknown for the case 1 < p1, . . . , pm < n/(n− 1). In 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 when ~ f = (f1, . . . , fm) with each fj ∈ W 1,pj (Ω) for some pj ∈ (1,∞). 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：

Zhang Xiao, Liu Feng, Zhang Huiyun

链接：

https://www.semanticscholar.org/paper/REGULARITY-OF-THE-LOCAL-MULTILINEAR-FRACTIONAL-AND-Zhang-Liu/e32832ba1fb637cacf2b42153856e91c2574a26a