Bounded double square functions

Pipher, Jill. "Bounded double square functions." Annales de l'institut Fourier 36.2 (1986): 69-82. <http://eudml.org/doc/74717>.

@article{Pipher1986,
abstract = {We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For $f\in L^ 1_\{loc\}(\{\bf R\}^ 2)$, we determine the sharp order of local integrability obtained when the square function of $f$ is in $L^\{\infty \}$. The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of $C_ p$ in $\Vert f\Vert _ p\le C_ p\Vert Sf\Vert _ p$.},
author = {Pipher, Jill},
journal = {Annales de l'institut Fourier},
keywords = {Calderòn-Torchinsky decomposition; double dyadic martingales; vector- valued form of an inequality for dyadic martingales},
language = {eng},
number = {2},
pages = {69-82},
publisher = {Association des Annales de l'Institut Fourier},
title = {Bounded double square functions},
url = {http://eudml.org/doc/74717},
volume = {36},
year = {1986},
}

TY - JOUR
AU - Pipher, Jill
TI - Bounded double square functions
JO - Annales de l'institut Fourier
PY - 1986
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 2
SP - 69
EP - 82
AB - We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For $f\in L^ 1_{loc}({\bf R}^ 2)$, we determine the sharp order of local integrability obtained when the square function of $f$ is in $L^{\infty }$. The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of $C_ p$ in $\Vert f\Vert _ p\le C_ p\Vert Sf\Vert _ p$.
LA - eng
KW - Calderòn-Torchinsky decomposition; double dyadic martingales; vector- valued form of an inequality for dyadic martingales
UR - http://eudml.org/doc/74717
ER -