Geodesic
Weighted inequalities for integral operators with some homogeneous kernels
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 423-432 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 BMO}}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb R^n)$.
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 BMO}}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb R^n)$.
Classification : 42A50, 42B20, 42B25
Keywords: weights; integral operators 
@article{CMJ_2005_55_2_a11,
     author = {Riveros, Mar{\'\i}a Silvina and Urciuolo, Marta},
     title = {Weighted inequalities for integral operators with some homogeneous kernels},
     journal = {Czechoslovak Mathematical Journal},
     pages = {423--432},
     year = {2005},
     volume = {55},
     number = {2},
     mrnumber = {2137148},
     zbl = {1081.42018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a11/}
}
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Riveros, María Silvina; Urciuolo, Marta. Weighted inequalities for integral operators with some homogeneous kernels. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 423-432. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a11/