Remarks on the Hilbert transform and on some families of multiplier operators related to it.

Laeng, Enrico. "Remarks on the Hilbert transform and on some families of multiplier operators related to it.." Collectanea Mathematica 58.1 (2007): 25-44. <http://eudml.org/doc/41794>.

@article{Laeng2007,
abstract = {We give an overview of the behavior of the classical Hilbert Transform H seen as an operator on Lp(R) and on weak-Lp(R), then we consider other operators related to H. In particular, we discuss various versions of Discrete Hilbert Transform and Fourier multipliers periodized in frequency, giving some partial results and stating some conjectures about their sharp bounds Lp(R) → Lp(R), for 1 &lt; p &lt; ∞.},
author = {Laeng, Enrico},
journal = {Collectanea Mathematica},
keywords = {Análisis de Fourier; Multiplicadores; Transformada de Hilbert},
language = {eng},
number = {1},
pages = {25-44},
title = {Remarks on the Hilbert transform and on some families of multiplier operators related to it.},
url = {http://eudml.org/doc/41794},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Laeng, Enrico
TI - Remarks on the Hilbert transform and on some families of multiplier operators related to it.
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 1
SP - 25
EP - 44
AB - We give an overview of the behavior of the classical Hilbert Transform H seen as an operator on Lp(R) and on weak-Lp(R), then we consider other operators related to H. In particular, we discuss various versions of Discrete Hilbert Transform and Fourier multipliers periodized in frequency, giving some partial results and stating some conjectures about their sharp bounds Lp(R) → Lp(R), for 1 &lt; p &lt; ∞.
LA - eng
KW - Análisis de Fourier; Multiplicadores; Transformada de Hilbert
UR - http://eudml.org/doc/41794
ER -