Carleson's Theorem: proof, complements, variations.

Lacey, Michael T.. "Carleson's Theorem: proof, complements, variations.." Publicacions Matemàtiques 48.2 (2004): 251-307. <http://eudml.org/doc/41502>.

@article{Lacey2004,
abstract = {Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given.},
author = {Lacey, Michael T.},
journal = {Publicacions Matemàtiques},
keywords = {Series de Fourier; Convergencia puntual; Integrales singulares; pointwise convergence; Fourier series; singular integrals; phase plane analysis; truncated Fourier transform},
language = {eng},
number = {2},
pages = {251-307},
title = {Carleson's Theorem: proof, complements, variations.},
url = {http://eudml.org/doc/41502},
volume = {48},
year = {2004},
}

TY - JOUR
AU - Lacey, Michael T.
TI - Carleson's Theorem: proof, complements, variations.
JO - Publicacions Matemàtiques
PY - 2004
VL - 48
IS - 2
SP - 251
EP - 307
AB - Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given.
LA - eng
KW - Series de Fourier; Convergencia puntual; Integrales singulares; pointwise convergence; Fourier series; singular integrals; phase plane analysis; truncated Fourier transform
UR - http://eudml.org/doc/41502
ER -