On the generalization of the Riesz¿Zygmund theorem for the ergodic Hilbert transform

• Autores: Lasha Ephremidze, Ryotaro Sato
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 1, 2007, págs. 113-122
• Idioma: inglés
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• Resumen

  • A reverse weak type inequality for the conjugate function is generalized to the ergodic case. The inequality allows us to prove the Riesz¿Zygmund theorem (if $f\geq 0$ and $f,\widetilde{f}\in L$, then $f\in L\log L$) for the ergodic Hilbert transform.