Integral restriction for bilinear operators

We consider the integral domain restriction operator TΩ for certain bilinear operator T. We obtain that if (s, p₁, p₂) satisfies 1/P¹ + 1/P² ≥  2/min{1,s) and ||T || L^P1 x L^P2 → L^s < ∞.

For some special domain Ω, this property holds for triplets (s, p₁, p₂₎ satisfying 1/P¹ + 1/P² ≥  1/min{1,s).