Carleson's theorem with quadratic phase functions

Michael T. Lacey. "Carleson's theorem with quadratic phase functions." Studia Mathematica 153.3 (2002): 249-267. <http://eudml.org/doc/286481>.

@article{MichaelT2002,
abstract = {It is shown that the operator below maps $L^\{p\}$ into itself for 1 < p < ∞. $Cf(x) := sup_\{a,b\} |p.v. ∫ f(x-y)e^\{i(ay²+by)\} dy/y|$. The supremum over b alone gives the famous theorem of L. Carleson [2] on the pointwise convergence of Fourier series. The supremum over a alone is an observation of E. M. Stein [12]. The method of proof builds upon Stein’s observation and an approach to Carleson’s theorem jointly developed by the author and C. M. Thiele [7].},
author = {Michael T. Lacey},
journal = {Studia Mathematica},
keywords = {oscillatory maximal integrals; polynomial phase; maximal operator; Hilbert transform; boundedness; Carleson-Hunt theorem},
language = {eng},
number = {3},
pages = {249-267},
title = {Carleson's theorem with quadratic phase functions},
url = {http://eudml.org/doc/286481},
volume = {153},
year = {2002},
}

TY - JOUR
AU - Michael T. Lacey
TI - Carleson's theorem with quadratic phase functions
JO - Studia Mathematica
PY - 2002
VL - 153
IS - 3
SP - 249
EP - 267
AB - It is shown that the operator below maps $L^{p}$ into itself for 1 < p < ∞. $Cf(x) := sup_{a,b} |p.v. ∫ f(x-y)e^{i(ay²+by)} dy/y|$. The supremum over b alone gives the famous theorem of L. Carleson [2] on the pointwise convergence of Fourier series. The supremum over a alone is an observation of E. M. Stein [12]. The method of proof builds upon Stein’s observation and an approach to Carleson’s theorem jointly developed by the author and C. M. Thiele [7].
LA - eng
KW - oscillatory maximal integrals; polynomial phase; maximal operator; Hilbert transform; boundedness; Carleson-Hunt theorem
UR - http://eudml.org/doc/286481
ER -