Some weighted norm inequalities for a one-sided version of $g{*}_{\lambda }$

L. de Rosa, and C. Segovia. "Some weighted norm inequalities for a one-sided version of $g*_{λ}$." Studia Mathematica 176.1 (2006): 21-36. <http://eudml.org/doc/284771>.

@article{L2006,
abstract = {We study the boundedness of the one-sided operator $g⁺_\{λ,φ\}$ between the weighted spaces $L^\{p\}(M¯w)$ and $L^\{p\}(w)$ for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of $g⁺_\{λ,φ\}$. For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of $g⁺_\{λ,φ\}$ from $L^\{p\}((M¯)^\{[p/2]+1\} w)$ to $L^\{p\}(w)$, where $(M¯)^\{k\}$ denotes the operator M¯ iterated k times.},
author = {L. de Rosa, C. Segovia},
journal = {Studia Mathematica},
keywords = {one-sided maximal functions; Littlewood–Paley theory; one-sided weights},
language = {eng},
number = {1},
pages = {21-36},
title = {Some weighted norm inequalities for a one-sided version of $g*_\{λ\}$},
url = {http://eudml.org/doc/284771},
volume = {176},
year = {2006},
}

TY - JOUR
AU - L. de Rosa
AU - C. Segovia
TI - Some weighted norm inequalities for a one-sided version of $g*_{λ}$
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 1
SP - 21
EP - 36
AB - We study the boundedness of the one-sided operator $g⁺_{λ,φ}$ between the weighted spaces $L^{p}(M¯w)$ and $L^{p}(w)$ for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of $g⁺_{λ,φ}$. For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of $g⁺_{λ,φ}$ from $L^{p}((M¯)^{[p/2]+1} w)$ to $L^{p}(w)$, where $(M¯)^{k}$ denotes the operator M¯ iterated k times.
LA - eng
KW - one-sided maximal functions; Littlewood–Paley theory; one-sided weights
UR - http://eudml.org/doc/284771
ER -