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Your search keyword '"Nie, Xudong"' showing total 9 results
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9 results on '"Nie, Xudong"'

1. Rearrangement inequalities of the one-dimensional maximal functions associated with general measures

Author

Nie, Xudong, Wu, Di, and Wang, Panwang

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

We prove a rearrangement inequality for the uncentered Hardy-Littlewood maximal function $M_{\mu}$ associate to general measure $\mu$ on $\mathbb{R}$. This inequality is analogous to the Stein's result $cf^{**}(t)\leq(Mf)^{*}(t)\leq C f^{**}(t)$, where $f^*$ is the symmetric decreasing rearrangement function of $f$ and $f^{**}(t)=\int_0^tf^*(x)dx$. Moreover, we compute the best constant of $M_{\mu}$ on $L^{p,\infty}(\mathbb{R},d\mu)$.

Published
2023

3. The dimension-free estimate for the truncated maximal operator

Author

Nie Xudong and Wang Panwang

Subjects
maximal function, dimension-free estimate, fourier multiplier, 42b20, 42b25, Mathematics, QA1-939
Abstract

We mainly study the dimension-free Lp{L}^{p}-inequality of the truncated maximal operator Mnaf(x)=supt>01∣Ba1∣∫Ba1f(x−ty)dy,{M}_{n}^{a}f\left(x)=\mathop{\sup }\limits_{t\gt 0}\frac{1}{| {B}_{a}^{1}| }\left|\mathop{\int }\limits_{{B}_{a}^{1}}f\left(x-ty){\rm{d}}y\hspace{-0.25em}\right|, where Ba1={x:a≤∣x∣≤1}{B}_{a}^{1}=\left\{x:a\le | x| \le 1\right\}. When 0≤an/(n−1)p\gt n\hspace{0.1em}\text{/}\hspace{0.1em}\left(n-1). When a=1a=1, we prove that ‖Mn1‖Lp(Rn)≤C(p)‖f‖Lp(Rn)\Vert {M}_{n}^{1}{\Vert }_{{L}^{p}\left({{\mathbb{R}}}^{n})}\le C\left(p)\Vert f{\Vert }_{{L}^{p}\left({{\mathbb{R}}}^{n})} for p≥2p\ge 2.

Published
2022
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9. Spinel type MCo2O4(M = Mn, Mg, Ni, Cu, Fe and Zn) for chemoresistance gas sensors

Author

Zheng, Zichen, Liu, Kewei, Zhou, Yiwen, Zhang, Zicong, Su, Hongyuan, Nie, Xudong, Debliquy, Marc, Yu, Zexin, and Zhang, Chao

Abstract

Gas sensors present significant research value and broad applicability for environmental monitoring, medical diagnosis and agricultural production. As a p-type spinel ternary semiconductor metal oxide (SMOX), MCo2O4(M = Mn, Mg, Ni, Cu, Fe and Zn) chemoresistance gas sensors possess a satisfactory sensing performance to diverse hazardous gases. Owning to the superior potential and widespread applications, this work provides a critical review of the current development for MCo2O4chemoresistance gas sensors. Basic information of MCo2O4and evaluation criteria of corresponding gas sensors were described primarily. Then the synthesis, morphology, characterization and sensing properties of MCo2O4gas sensors were elaborated on the basis of different microtopography dimensions under zero dimension (0D), one dimension (1D), two dimension (2D) and three dimension (3D). Various efficient tactics for improving sensing performance and relevant transducing mechanism were demonstrated as well. Finally, perspectives on developing MCo2O4synthesis and applications in gas sensors were elaborated.

Published
2024
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