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 < p < ∞.
@article{urn:eudml:doc:41794,
title = {Remarks on the Hilbert transform and on some families of multiplier operators related to it.},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {25-44},
zbl = {1135.42006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41794}
}
Laeng, Enrico. Remarks on the Hilbert transform and on some families of multiplier operators related to it.. Collectanea Mathematica, Tome 58 (2007) pp. 25-44. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41794/