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452 results on '"Wu, Xinfeng"'

1. Singular Integrals associated with Reflection Groups on Euclidean Space

Author

Han, Yongsheng, Li, Ji, Tan, Chaoqiang, Wang, Zipeng, and Wu, Xinfeng

Subjects
Mathematics - Classical Analysis and ODEs
Abstract

In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the study of singular integrals to include the effects of group reflections on Euclidean space, and to establish the T1 theorem for these singular integrals.

Published
2024

6. The Kato-Ponce Inequality with Polynomial Weights

Author

Oh, Seungly and Wu, Xinfeng

Subjects
Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 42B20 (Primary), 46E35 (Secondary)
Abstract

We consider various versions of fractional Leibniz rules (also known as Kato-Ponce inequalities) with polynomial weights $\langle x\rangle^a = (1+|x|^2)^{a/2}$ for $a\ge 0$. We show that the weighted Kato-Ponce estimate with the inhomogeneous Bessel potential $J^s = (1- \De)^{{s}/{2}}$ holds for the full range of bilinear Lebesgue exponents, for all polynomial weights, and for the sharp range of the degree $s$. This result, in particular, demonstrates that neither the classical Muckenhoupt weight condition nor the more general multilinear weight condition is required for the weighted Kato-Ponce inequality. We also consider a few other variants such as commutator and mixed norm estimates, and analogous conclusions are derived. Our results contain strong-type inequalities for both $L^1$ and $L^\infty$ endpoints, which extend several existing results.

Published
2021

8. Estimates of Cauchy–Szegö Kernel in Hardy Spaces on Nilpotent Lie Groups of Step Two

Author

Wu, Xinfeng, Chang, Der-Chen, Han, Yongsheng, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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12. Variational Inequalities for Bilinear Averaging Operators over Convex Bodies

Author

Ding, Yong, Hong, Guixiang, and Wu, Xinfeng

Subjects
Mathematics - Classical Analysis and ODEs, 42B25, 47B38, 47A35, 47D07
Abstract

We study $q$-variation inequality for bilinear averaging operators over convex bodies $(G_t)_{t>0}$ defined by \begin{align*} \mathbf{A}_t^G(f_1,f_2)(x) & =\frac{1}{|G_t|}\int_{G_t} f_1(x+y_1)f_2(x+y_2)\, dy_1\, dy_2, \quad x\in \Bbb R^d. \end{align*} where $G_t$ are the dilates of a convex body $G$ in $\Bbb R^{2d}$. We prove that $$\|V_q(\mathbf{A}_t^G(f_1,f_2): t>0) \|_{L^p} \lesssim \|f_1\|_{L^{p_1}} \|f_2\|_{L^{p_2}},$$ for $2

Published
2019

34. Smoothing Properties of Bilinear Operators and Leibniz-Type Rules in Lebesgue and Mixed Lebesgue Spaces

Author

Hart, Jarod, Torres, Rodolfo H., and Wu, Xinfeng

Subjects
Mathematics - Classical Analysis and ODEs, Primary: 42B20, Secondary: 42B15, 47G99
Abstract

We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain several Leibniz-type rules in the contexts of Lebesgue and mixed Lebesgue spaces.

Published
2017

37. Relations between product and flag Triebel-Lizorkin spaces.

Author

Cao, Yannan, Chang, Der-Chen, and Wu, Xinfeng

Subjects
HARDY spaces, INTEGRAL operators
Abstract

Nagel, Ricci and Stein proved that product kernels are finite sums of flag kernels in the Euclidean space. We show that the product Triebel-Lizorkin space is the intersection of two flag Triebel-Lizorkin spaces. This extends a main result in [Chang D-C, Han Y, Wu X. Relations between product and flag Hardy spaces. J Geom Anal. 2021;31(7):6601–6623]. As an application, we provide a new proof of the boundedness of product singular integral operators on product Triebel-Lizorkin spaces. [ABSTRACT FROM AUTHOR]

Published
2024
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38. Excellent thermal conductive epoxy composites via adding UHMWPE fiber obtained by hot drawing method.

Author

Shi, Shanshan, Jiang, Tao, Wang, Ying, Sun, Yongfei, Cao, Shuai, Gui, Xiaofan, Li, Yifan, Yu, Wei, Lin, Donghai, Xie, Huaqing, Li, Xiaofeng, Li, Wenge, Sun, Kai, Yu, Jinhong, and Wu, Xinfeng

Subjects
THERMAL conductivity, PHONON scattering, HEAT capacity, THERMAL properties, ELECTRIC conductivity
Abstract

The continuous updating and iteration of electronic devices brings about a significant accumulation of heat. It is urgent to enhance the thermal properties of polymer‐based composites to alleviate the heat dissipation problem in the microelectronics industry. In this paper, the hot drawing process was introduced to increase the crystallinity of ultra‐high molecular weight polyethylene (UHMWPE) fiber and improve its thermal conductivity. The ultra‐high molecular weight polyethylene fiber/epoxy resin (UHMWPE fiber/Epoxy) composites with high thermal conductivity were prepared by compositing UHMWPE fiber with epoxy resin under vacuum conditions. Due to the good crystallinity of the UHMWPE fiber (86%), an efficient thermal conduction path is provided for phonons in the axial direction along the fibers. The results show that the thermal conductivity of the composites reaches a maximum of 3.51 W/mK (in‐plane), which is 17.47 times higher than that of the epoxy resin (0.19 W/mK). The thermography pictures indicate that the composites have better heat transfer capacity with an increase in the draw ratio (λ). In addition, the composites also have the characteristics of low density and low electrical conductivity. These researches will provide a new idea for the preparation of all‐polymer composites with high thermal properties. Highlights: A hot drawing process was introduced to increase the crystallinity of UHMWPE fiber for improving thermal conductivity.High crystallinity facilitates the reduction of phonon scattering and the transmission of thermal energy by phonons.The obtained polymer composites exhibit an ultra‐high in‐plane thermal conductivity. [ABSTRACT FROM AUTHOR]

Published
2024
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39. Construction of Frames Using Calderón–Zygmund Operator Theory

Author

Chang, Der-Chen, Han, Yongsheng, Wu, Xinfeng, Benedetto, John J., Series Editor, Aldroubi, Akram, Editorial Board Member, Cochran, Douglas, Editorial Board Member, Feichtinger, Hans G., Editorial Board Member, Heil, Christopher, Editorial Board Member, Jaffard, Stéphane, Editorial Board Member, Kovačević, Jelena, Editorial Board Member, Kutyniok, Gitta, Editorial Board Member, Maggioni, Mauro, Editorial Board Member, Shen, Zuowei, Editorial Board Member, Strohmer, Thomas, Editorial Board Member, Wang, Yang, Editorial Board Member, Hirn, Matthew, editor, Li, Shidong, editor, Okoudjou, Kasso A., editor, Saliani, Sandra, editor, and Yilmaz, Özgür, editor

Published
2021
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40. Sandwich-Structured Thermal Interface Materials with High Thermal Conductivity

Author

Xu, Kang, primary, Zhang, Zhenbang, additional, Wang, Yandong, additional, Li, Maohua, additional, Chen, Yapeng, additional, Kong, Xiangdong, additional, Zhang, Jianxiang, additional, Yang, Rongjie, additional, Li, Linhong, additional, Zhou, Yiwei, additional, Gong, Ping, additional, Qin, Yue, additional, Cao, Yong, additional, Cai, Tao, additional, Lin, Cheng-Te, additional, Jiang, Nan, additional, Wu, Xinfeng, additional, and Yu, Jinhong, additional

Published
2024
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