Revisiting the Marcinkiewicz theorem for non-commutative maximal functions

• Autores: Léonard Cadilhac, Eric Ricard
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 69, Nº 1, 2025, págs. 195-216
• Idioma: inglés
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• Resumen

  • We give an alternative proof of a Marcinkiewicz interpolation theorem for non-commutative maximal functions and positive maps and refine earlier versions of the statement. The main novelty is that it provides a substitute for the maximal function of a martingale in Lp, 1 < p 6 ∞, losing very little on numerical constants. For non-positive maps, the above mentioned theorem fails but we can still obtain some interpolation results by weakening the maximal norm that we consider.