Approximation of the image of the L _p ball under Hilbert-Schmidt integral operator

Abstract

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