# Sharp bounds for fractional type operators with $L^{\alpha,s}$-Hörmander conditions

## DOI:

https://doi.org/10.33044/revuma.2211## Abstract

We provide the sharp bound for a fractional type operator given by a kernel satisfying the $L^{\alpha,s}$-Hörmander condition and certain fractional size condition, $0 < \alpha < n$ and $1 < s\leq \infty$. In order to prove this result we use a new appropriate sparse domination. Examples of these operators include the fractional rough operators. For the case $s=\infty$ we recover the sharp bound of the fractional integral, $I_{\alpha}$, proved by Lacey et al. [*J. Functional Anal.* **259** (2010), no. 5, 1073–1097].

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