On a class of sharp Sobolev type estimates with weights

Raul Hindov, Evgeniy Lokharu

We study sharp weighted Sobolev-type inequalities of the form\[ \int_{0}^{1}|u(x)|ρ(x) \,\mathrm{d}x \leqslant Λ \Bigl(\int_{0}^{1}|u^{(k)}(x)|^2 \,\mathrm{d}x \Bigr)^{1/2}, \qqu…