Stability for analytic Hardy spaces

Abstract

As we have seen (and much more evidence to this will be given in Part 2 of this book), Calderón–Zygmund-type decompositions are a universal tool for constructing near-minimizers and proving their stability. However, there is a price to be paid for generality: some natural questions remain beyond the capacity of this method. We have already encountered a question of this sort, namely, the case of an infinite exponent in the scale of Lebesgue spaces, see §3 in Chapter 3.