On Doob’s inequality and Burkholder’s inequality in weak spaces

• Autores: Masato Kikuchi
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 3, 2016, págs. 461-483
• Idioma: inglés
• DOI: 10.1007/s13348-015-0153-z
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• Resumen

  • Let X be a Banach function space over a nonatomic probability space. We associate with X the weak space {\mathrm {w}}\text {-}{X}, which is a quasi-Banach space defined in a natural way. We give necessary and sufficient conditions for Doob’s inequality in {\mathrm {w}}\text {-}{X} to be valid, and necessary and sufficient conditions for Burkholder’s inequality in {\mathrm {w}}\text {-}{X} to be valid.