From restricted weak type to strong type estimates

• Autores: María Jesús Carro Rossell
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 70, Nº 3, 2004, págs. 750-762
• Idioma: inglés
• DOI: 10.1112/s0024610704005812
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• Resumen

  • Let be a sublinear operator such that for some positive function and every measurable set . Then it is shown that under some conditions on the operator , this restricted weak type estimate can be extended to the set of all functions such that , in the sense that . This inequality allows strong type estimates for to be obtained on several classes of spaces, such as logarithmic spaces and Lorentz spaces. A similar problem for operators acting on radial functions is also studied.