Some sufficient conditions for embedding a weighted Sobolev class on a John domain
Anastasia Andreevna Vasil'eva · Siberian Mathematical Journal · 2015
We obtain some sufficient conditions for embedding weighted Sobolev classes on a John domain into weighted Lebesgue spaces. The weights are functions of the distance to some h -set on the boundary of the domain. The problem reduces to estimating the norms of two-weighted summation operators on a certain tree. We then apply our previous results on these estimates.