Hölder inequality for functions that are integrable with respect to bilinear maps

• Autores: Óscar Blasco de la Cruz , José Manuel Calabuig Rodríguez
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 102, Nº 1, 2008, págs. 101-110
• Idioma: inglés
• DOI: 10.7146/math.scand.a-15053
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• Resumen

  • Let (Ω,Σ,μ) be a finite measure space, 1≤p<∞, X be a Banach space X and B:X×Y→Z be a bounded bilinear map. We say that an X-valued function f is p-integrable with respect to B whenever sup∥y∥=1∫Ω∥B(f(w),y)∥pdμ<∞. We get an analogue to Hölder's inequality in this setting.