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

• Autores: Gen Nakamura, Kazuo Hashimoto
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 65, Fasc. 3, 2014, págs. 407-416
• Idioma: inglés
• DOI: 10.1007/s13348-013-0099-y
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• Resumen

  • 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??(?,?)<∞ .