Inequalities for the truncated Hilbert transform and the segment multiplier

• Autores: Adam Osekowski
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 65, Fasc. 1, 2014, págs. 103-118
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • The paper is devoted to the study of LlogL inequalities and other related bounds for two classical operators on the real line: the truncated Hilbert transform and the segment multiplier. Using duality, these estimates are deduced from corresponding sharp exponential-type bounds, the proofs of which rest on the construction of appropriate harmonic functions on the strip [−1,1]×ℝ and transference-type arguments.