  We present complete classifications of automorphisms of two closed
subalgebras of the bounded analytic functions on the open unit disc
$\mathbb{D}$, namely, the subalgebra of functions vanishing at the origin, and
the subalgebra of functions whose first derivative vanishes at the origin. The
later subalgebra is known as the Neil algebra. We also characterize generalized
tri-circular projections on $H^{p}(\mathbb{D})$ and $H^{p}(\mathbb{D}^2)$,
$1\leq p \leq \infty$, $p\neq 2$.

Complex Variables;Functional Analysis;Operator Algebras