arXiv subjects

Luciana Melchiori

Publications and source records attributed to Luciana Melchiori.

2 recordsLinked to original sources

arXiv2019

Musielak Orlicz bumps and Bloom type estimates for commutators of Calderón Zygmund and fractional integral operators on variable Lebesgue spaces via sparse operators

We obtain Musielak Orlicz bumps conditions on a pair of weights for the boundedness of Calderón Zygmund operators and their commutators between variable Lebesgue spaces with different weights. The symbols of the commutators belong to a wider class of functions. We also give Bloom type estimates for commutators of Calderón Zygmund and fractional integral operators in the variable Lebesgue context. The techniques involved in both type of results are related with the theory of sparse domination.

math.AP↗

arXiv2019

Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights

We prove that a generalized Fefferman-Phong type condition on a pair of weights $u$ and $v$ is sufficient for the boundedness of the commutators of potential type operators from $L^{p(\cdot)}_v$ into $L^{q(\cdot)}_u$. We also give an improvement of this result in the sense that we not only consider a variable version of power bump conditions, but also weaker norms related to Musielak-Orlicz functions. We consider a wider class of symbols including Lipschitz symbols and some generalizations.

math.CA↗