We find necessary and sufficient conditions on the function Φfor the inequality (Formula presented.) to be true. Here Kis a positively homogeneous of order α-d, possibly vector valued, kernel, Φis a p-homogeneous function, and p=d/(d-α). The domain Ω⊂Rdis either bounded with C1,βsmooth boundary for some β>0or a half-space in Rd. As a corollary, we describe the positively homogeneous of order d/(d-1)functions Φ:Rd→Rthat are suitable for the bound (Formula presented.) Bibliography:16 titles.