# Two weighted inequalities for convolution maximal operators.

• Volume: 46, Issue: 1, page 119-138
• ISSN: 0214-1493

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## Abstract

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Let φ: R → [0,∞) an integrable function such that φχ(-∞,0) = 0 and φ is decreasing in (0,∞). Let τhf(x) = f(x-h), with h ∈ R {0} and fR(x) = 1/R f(x/R), with R &gt; 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτhφf(x) = supR&gt;0|f| * [τhφ]R(x) are of weak type (p, p) with respect to (u, v), 1 &lt; p &lt; ∞.

## How to cite

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Bernardis, Ana Lucía, and Martín-Reyes, Francisco Javier. "Two weighted inequalities for convolution maximal operators.." Publicacions Matemàtiques 46.1 (2002): 119-138. <http://eudml.org/doc/41446>.

@article{Bernardis2002,
abstract = {Let φ: R → [0,∞) an integrable function such that φχ(-∞,0) = 0 and φ is decreasing in (0,∞). Let τhf(x) = f(x-h), with h ∈ R \{0\} and fR(x) = 1/R f(x/R), with R &gt; 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτhφf(x) = supR&gt;0|f| * [τhφ]R(x) are of weak type (p, p) with respect to (u, v), 1 &lt; p &lt; ∞.},
author = {Bernardis, Ana Lucía, Martín-Reyes, Francisco Javier},
journal = {Publicacions Matemàtiques},
keywords = {Operador maximal de Hardy-Littlewood; Littlewood-Paley; Convolución; Desigualdades; weighted inequalities; convolution maximal operators; class; Sawyer's classes},
language = {eng},
number = {1},
pages = {119-138},
title = {Two weighted inequalities for convolution maximal operators.},
url = {http://eudml.org/doc/41446},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Bernardis, Ana Lucía
AU - Martín-Reyes, Francisco Javier
TI - Two weighted inequalities for convolution maximal operators.
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - 1
SP - 119
EP - 138
AB - Let φ: R → [0,∞) an integrable function such that φχ(-∞,0) = 0 and φ is decreasing in (0,∞). Let τhf(x) = f(x-h), with h ∈ R {0} and fR(x) = 1/R f(x/R), with R &gt; 0. In this paper we characterize the pair of weights (u, v) such that the operators Mτhφf(x) = supR&gt;0|f| * [τhφ]R(x) are of weak type (p, p) with respect to (u, v), 1 &lt; p &lt; ∞.
LA - eng
KW - Operador maximal de Hardy-Littlewood; Littlewood-Paley; Convolución; Desigualdades; weighted inequalities; convolution maximal operators; class; Sawyer's classes
UR - http://eudml.org/doc/41446
ER -

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