The Mazur product map on Hardy-type sequence spaces

We study certain Hardy-type sequence spaces Hp and , 1⩽p⩽∞, which are analogues of ℓ∞ and c0, respectively. We show that the Mazur product is not onto for every p∈(1,∞) with q=p−1(p−1). We present corollaries for spaces defined via weighted ℓp seminorms and for c0. The latter corollary provides a new solution of Mazur's Problem 8 in the Scottish Book.