The spaces 𝐻^{𝑝}(𝐵_{𝑛}),0<𝑝<1, and 𝐵_{𝑝𝑞}(𝐵_{𝑛}),0<𝑝<𝑞<1, are not locally convex

Abstract

ABSTRACT. In this note, we use the Ryll-Wojtaszczyk polynomials to prove that the spaces HP(Bn), 0 < p < 1, and Bpq{Bn), 0 < p < q < 1, fail to be locally convex.