Some weighted norm inequalities for a one-sided version of g * λ

L. de Rosa; C. Segovia

Studia Mathematica (2006)

  • Volume: 176, Issue: 1, page 21-36
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.