Approximation of the image of the $L_p$ ball under Hilbert-Schmidt integral operator

Abstract

In this paper an approximation of the image of the closed ball of the space $L_p$ $(p>1)$ centered at the origin with radius $r$ under Hilbert-Schmidt integral operator $F( \cdot ):L_p\rightarrow L_q$, $\frac{1}{p}+\frac{1}{q}=1,$ is considered. An error evaluation for given approximation is obtained.