arXiv subjects

M. Silvina Riveros

Publications and source records attributed to M. Silvina Riveros.

2 recordsLinked to original sources

arXiv2026

Weighted $H^p-L^q$ boundedness of integral operators with rough kernels

In this paper, we study integral operators \begin{equation*} T_αf(x)=\int_{\mathbb{R}^{n}}K(x,y) f(y)dy, \end{equation*} with kernels $K(x,y)= k_1( x- A_1y)...k_m( x-A_my),$ where $k_i(x)=\frac{Ω_i(x)}{|x|^{n/q_i}}$ and $Ω_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions of degree zero, satisfying a size and a Dini condition, $A_{i}$ are certain invertible matrices, and $\frac n{q_1}+\dots+\frac n{q_m}=n-α,$ $0\leq α<n.$ We obtain the $H^{p}_{w^p}(\mathbb{R}^{n})-L^{q}_{w^q}(\mathbb{R}^{n})$ boundedness of these operators, for a class of Muckenhoupt weights $w$, satisfying the condition \begin{equation*} w(A_ix)\leq cw(x), \end{equation*} $a.e.x\in\mathbb{R} ^n $, $1\leq i\leq m$.

math.CA↗

arXiv2026

Characterization of weights for the variable fractional maximal operator and weighted inequalities for variable fractional rough operators

We characterize the class of weights related to the boundedness of variable fractional maximal operator $M_{β(\cdot),r(\cdot)}$ on variable Lebesgue spaces. This extend previously known results, including those corresponding to the fractional operator $M_{β(\cdot),1}$. In addition, we introduce a class of kernels $K$ satisfying a new variable Hörmander-type condition $H_{β(\cdot),r(\cdot)}$. For the fractional operator $T_{β(\cdot)}$ given by a kernel in $H_{β(\cdot),r(\cdot)}$, we prove a Coifman-Fefferman inequality and weighted inequalities in variable Lebesgue space. Finally, we provide examples of kernels in this variable Hörmander class.

math.FA↗