In this lecture, we shall discuss a question whether the density of analytic polynomials in an H-admissible space is sufficient to the minimality of the space? This question has a purely foundational background, relating fundamental concepts from the theory of Hp spaces. We solve this problem by finding suitable counterexamples of Hardy spaces built upon some weighted Lebesgue spaces. In particular, we provide a direct construction of weights from Szegö’s class, which guarantees the existence of isomorphic copies of l∞ in weighted Hardy spaces on the unit disc.
Radosaw Szwedek
Adam Mickiewicz University, Poznan
Faculty of Mathematics and Computer Science
szwedek@amu.edu.pl
