Approximation of the image of the Lp ball under Hilbert-Schmidt integral operator

In this article, an approximation of the image of the closed ball of the space Lp{L}_{p} (p>1p\gt 1) centered at the origin with radius rr under Hilbert-Schmidt integral operator F(⋅):Lp→LqF\left(\cdot ):{L}_{p}\to {L}_{q}, 1p+1q=1\frac{1}{p}+\frac{1}{q}=1 is considered. An error evaluation for the given approximation is obtained.