Weighted bounds for variational Fourier series

Yen Do, and Michael Lacey. "Weighted bounds for variational Fourier series." Studia Mathematica 211.2 (2012): 153-190. <http://eudml.org/doc/285680>.

@article{YenDo2012,
abstract = {For 1 < p < ∞ and for weight w in $A_\{p\}$, we show that the r-variation of the Fourier sums of any function f in $L^\{p\}(w)$ is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational inequality of Lépingle.},
author = {Yen Do, Michael Lacey},
journal = {Studia Mathematica},
keywords = {Fourier series; pointwise convergence; weight; Lépingle inequality; Carleson},
language = {eng},
number = {2},
pages = {153-190},
title = {Weighted bounds for variational Fourier series},
url = {http://eudml.org/doc/285680},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Yen Do
AU - Michael Lacey
TI - Weighted bounds for variational Fourier series
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 2
SP - 153
EP - 190
AB - For 1 < p < ∞ and for weight w in $A_{p}$, we show that the r-variation of the Fourier sums of any function f in $L^{p}(w)$ is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational inequality of Lépingle.
LA - eng
KW - Fourier series; pointwise convergence; weight; Lépingle inequality; Carleson
UR - http://eudml.org/doc/285680
ER -