Resumen de On the essential bounded variation of ??(ℝ,?) -functions

Gen Nakamura, Kazuo Hashimoto

• Let ? be a Banach space. Nakamura and Hashimoto in (Proc Japan Acad Ser A 87:77–82, 2011), we showed that for every ?∈?1(ℝ) , limℎ→0∫ℝ∣∣∣?(?+ℎ)−?(?)ℎ∣∣∣??=ess?1(?).

  In this paper, we are concerned with the limit limℎ→0∫ℝ‖‖‖?(?+ℎ)−?(?)ℎ‖‖‖??? (*) for ?∈?loc1(ℝ,?) . We show that the limit (∗) coincides with the essential ? -variation of ? in the sense of F. Riesz, and we give characterizations of functions with bounded essential ? -variation, i.e, ess??(?,?)<∞ .