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
DOI: 10.1007/s13348-013-0086-3
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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.