  In this paper we formulate embedding maps into time-frequency space related
to the Carleson operator and its variational counterpart. We prove bounds for
these embedding maps by iterating the outer measure theory of [DT15].
Introducing iterated outer $L^p$ spaces is a main novelty of this paper.
  [DT15] Yen Do and Christoph Thiele. "$L^p$ theory for outer measures and two
themes of Lennart Carleson united". In: Bulletin of the American Mathematical
Society 52.2 (2015), pp. 249-296.
