19.3.14 Linear operators

condition: The operator \( A \) maps the space \( E_{1} \) into the space \( E_{2} \). Find the norm of the operator \(A\). Integral operator \begin{tabular}{|l|l|l|} \hline\( L_{2}[0,2] \) & \( L_{2}[0,1] \) & \( (A x)(t)=\int_{0}^{2}(t+1) s^{2} x\left(s^{2}\right) d s \) \\ \hline \end{tabular}