arXiv subjects

Tianyang He

Publications and source records attributed to Tianyang He.

3 recordsLinked to original sources

arXiv2026

The Weighted $\boldsymbol{L}^{\boldsymbol{p}}$ estimates for the fractional Hardy operator and a class of integral operators on the Heisenberg group

In the setting of a Heisenberg group, we first studied the sharp weak estimate for the $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Next, we studied the sharp bounds for the $m$-linear $n$-dimensional integral operator with a kernel on weighted Lebesgue spaces. As an application, the sharp bounds for Hardy, Hardy-Littlewood-P\'{o}lya, and Hilbert operators on weighted Lebesgue spaces were obtained. Finally, according to the previous steps, we also found the estimate for the Hausdorff operator on weighted $L^p$ spaces.

math.FA↗

arXiv2025

Sharp weak bounds for the Hardy-Littlewood-P\'{o}lya operator and the weak bounds for the multilinear integral operator

In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-P\'{o}lya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^{\beta} ) $ to weighted weak Lebesgue spaces $L^{q,\infty}(\mathbb{R} ^n,|x|^{\gamma})$. Next, we obtain the weak bounds for the $m$-linear $n$-dimensional integral operator.

math.CA↗

arXiv2025

Sharp bounds for the $\boldsymbol{p}$-adic $\boldsymbol{n}$-dimensional fractional Hardy operator and a class of integral operators on $\boldsymbol{p}$-adic function spaces

In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on $p$-adic weighted spaces $H_{\alpha}^{\infty}( \mathbb{Q} _{p}^{n} )$. As an application, the sharp bounds for $p$-adic Hardy and Hilbert operators on $p$-adic weighted spaces are obtained. Finally, we also find the sharp bound for the Hausdorff operator on $p$-adic weighted spaces, which generalizes the previous results.

math.FA↗