Absolutely minimum attaining Toeplitz and absolutely norm attaining Hankel operators

In this article, we completely characterize absolutely norm attaining Hankel operators and absolutely minimum attaining Toeplitz operators. We also improve \cite[Theorem 2.1]{RGSSSTOE1}, by characterizing the absolutely norm attaining Toeplitz operator $T_{\phi }$ in terms of the symbol $\phi \in L^{\mathrm{\infty }}$.