Level-set inequalities on fractional maximal distribution functions and applications to regularity theory

The aim of this paper is to establish an abstract theory based on the so-called fractional-maximal distribution functions (FMDs). From basic ideas introduced in [1], we develop and prove some results related level-set inequalities norm-comparisons by using language such FMDs. Particularly interesting applicability our approach that has been shown regularity Calderón-Zygmund type estimates. In paper, due research experience, will global estimates for two types general quasilinear problems (problems with divergence form double obstacles), via operators range applications these large. Apart from examples elliptic equations discussed, it also promising indicate further possible other special topics.