Weighted inequalities for integral operators with some homogeneous kernels

Riveros, María Silvina, and Urciuolo, Marta. "Weighted inequalities for integral operators with some homogeneous kernels." Czechoslovak Mathematical Journal 55.2 (2005): 423-432. <http://eudml.org/doc/30955>.

@article{Riveros2005,
abstract = {In this paper we study integral operators of the form \[ Tf(x)=\int | x-a\_1y|^\{-\alpha \_1\}\dots | x-a\_my|^\{-\alpha \_m\}f(y)\mathrm \{d\}y, \]$\alpha _1+\dots +\alpha _m=n$. We obtain the $L^p(w)$ boundedness for them, and a weighted $(1,1)$ inequality for weights $w$ in $A_p$ satisfying that there exists $c\ge 1$ such that $w( a_ix) \le cw( x)$ for a.e. $x\in \mathbb \{R\}^n$, $1\le i\le m$. Moreover, we prove $\Vert Tf\Vert _\{\{\mathrm \{B\}MO\}\}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb \{R\}^n)$.},
author = {Riveros, María Silvina, Urciuolo, Marta},
journal = {Czechoslovak Mathematical Journal},
keywords = {weights; integral operators; weights; integral operators; -boundedness},
language = {eng},
number = {2},
pages = {423-432},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weighted inequalities for integral operators with some homogeneous kernels},
url = {http://eudml.org/doc/30955},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Riveros, María Silvina
AU - Urciuolo, Marta
TI - Weighted inequalities for integral operators with some homogeneous kernels
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 423
EP - 432
AB - In this paper we study integral operators of the form \[ Tf(x)=\int | x-a_1y|^{-\alpha _1}\dots | x-a_my|^{-\alpha _m}f(y)\mathrm {d}y, \]$\alpha _1+\dots +\alpha _m=n$. We obtain the $L^p(w)$ boundedness for them, and a weighted $(1,1)$ inequality for weights $w$ in $A_p$ satisfying that there exists $c\ge 1$ such that $w( a_ix) \le cw( x)$ for a.e. $x\in \mathbb {R}^n$, $1\le i\le m$. Moreover, we prove $\Vert Tf\Vert _{{\mathrm {B}MO}}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb {R}^n)$.
LA - eng
KW - weights; integral operators; weights; integral operators; -boundedness
UR - http://eudml.org/doc/30955
ER -