Brennan Conjecture for Basin of Attraction at Infinity

This paper investigates the Brennan Conjecture for domains $\mathrm{\Omega }$ that arise as basins of attraction of a polynomial. We extend the result of Baranski, Volberg, and Zdunik to a broader class of polynomials. We prove that for any monic polynomial of degree $m$ with sufficiently small non-leading coefficients, Brennan Conjecture holds for its basin of attraction.