1. Weighted inequalities for integral operators with some homogeneous kernels
- Creator:
- Riveros, María Silvina and Urciuolo, Marta
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- weights and integral operators
- Language:
- English
- Description:
- 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 $f\in L^\infty ( \mathbb R^n)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public