Structure of a class of Lie conformal algebras of Block type

Let $p$ be a nonzero complex number. Recently, a class of infinite rank Lie conformal algebras $\mathfrak{B}(p)$ was introduced in [13]. In this paper, we study the structure theory of this class of Lie conformal algebras. Specifically, we completely determine the conformal derivations, the conformal biderivations and certain second cohomologies of $\mathfrak{B}(p)$.