arXiv subjects

María Silvina Riveros

Publications and source records attributed to María Silvina Riveros.

5 recordsLinked to original sources

arXiv2021

Sharp bounds for fractional operator with $L^{α,r'}$-Hörmander conditions

In this paper we prove the sharp boundedness for a fractional type operator given by a kernel that satisfy a $L^{α,r'}$-Hörmander conditions and a fractional size condition, where $0<α<n$ and $1< r'\leq \infty$. To prove this result we use a new appropriate sparse domination which we provide in this work. For the case $r'=\infty$ we recover the sharp boundedness for the fractional integral, $I_α$, proved in [Lacey, M. T., Moen, K., Pérez, C., Torres, R. H. (2010). Sharp weighted bounds for fractional integral operators. Journal of Functional Analysis, 259(5), 1073-1097.]

math.CA↗

arXiv2020

Necessary condition on the weight for maximal and integral operators with rough kernels

Let $0\leq α<n$, $m\in \mathbb{N}$ and let consider $T_{α,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies a fractional size and generalized fractional Hörmander condition. In [Ibañez-Firnkorn, G. H., and Riveros, M. S. (2018). Certain fractional type operators with Hörmander conditions. To appear in Ann. Acad. Sci. Fenn. Math.] it was proved that $T_{α,m}$ is controlled in $L^p(w)$-norms, $w\in A_{\infty}$, by the sum of maximal operators $M_{A_i^{-1},α}$. In this paper we present the class of weights $\mathcal{A}_{A,p,q}$, where $A$ is an invertible matrix. This class are the good weights for the weak-type estimate of $M_{A^{-1},α}$. For certain kernels $k_i$ we can characterize the weights for the strong-type estimate of $T_{α,m}$. Also, we give a the strong-type estimate using testing conditions.

math.CA↗

arXiv2018

Commutators of certain fractional type operators with Hörmander conditions, one-weighted and two-weighted inequalities

In this paper we study the commutators of fractional type integral operators. This operators are given by kernels of theform $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles matrices and each $k_i$ satisfies a fractional size condition and generalized fractional Hörmander condition. We obtain weighted Coifman estimates, weighted $L^p(w^p)$ - $L^q(w^q)$ estimates and weighted BMO estimates. We also give a two weight strong estimate for pair of weights of the form $(u,Su)$ where $u$ is an arbitrary non-negative function and $S$ is a maximal operator depending on the smoothness of the kernel $K$. For the singular case we also give a two-weighted endpoint estimate.

math.CA↗

arXiv2017

Hörmander's conditions for vector-valued kernels of singular integrals and its commutators

In this paper we study Coifman type estimates and weighted norm inequalities for singular integral operators $T$ and its commutators, given by the convolution with a vector valued kernel $K$. We define a weaker Hörmander type condition associated with Young functions for the vector valued kernels. With this general framework we obtain as an example the result for the square operator and its commutator given in [ M. Lorente, M.S. Riveros, A. de la Torre \emph{On the Coifman type inequality for the oscillation of the one-sided averages }, Journal of Mathematical Analysis and Applications, Vol 336, Issue 1,\ (2007) 577-592.]

math.CA↗

arXiv2013

Weighted inequalities related to a Muckenhoupt and Wheeden problem for one-side singular integrals

In this paper we obtain for $T^+$, a one-sided singular integral given by a Calderón-Zygmund kernel with support in $(-\infty,0)$, a $L^p(w)$ bound when $w\in A_1^+$. A. K. Lerner, S. Ombrosi, and C. Pérez proved in [ "$A_{1}$ Bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden", Math. Res. Lett. \textbf{16} (2009), no. 1, 149-156] that this bound is sharp with respect to $||w||_{A_1} $ and $p$ . We also give a $L^{1,\infty}(w)$ estimate, for a related problem of Muckenhoupt and Wheeden for $w\in A_1^+$ . We improve the classical results, for one-sided singular integrals, by putting in the inequalities a wider class of weights.

math.AP↗