Hu, Yin Yin Lu, Yu Feng Liu, Liu
Published in
Acta Mathematica Sinica, English Series

On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and su...

Nie, Yao Zheng, Xiao Xin
Published in
Acta Mathematica Sinica, English Series

This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier-Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data (u0, ω0) whose norm of FB˙1,q−1(q>2)\docu...

Wang, Yuan Qiao, Jian Yong Yang, Jing
Published in
Acta Mathematica Sinica, English Series

Professor Lo Yang is a world famous mathematician of our country. He made a lot of outstanding achievements in the value distribution theory of function theory, which are highly rated and widely quoted by domestic and foreign scholars. He also did a lot of work to develop Chinese mathematics. It can be said that Professor Yang is one of the mathema...

Yu, Xiao Hui
Published in
Acta Mathematica Sinica, English Series

In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition {−Δu+u=|u|r−2uin,∂u∂ν=|u|q−2uon∂,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} ...

Wu, Xiao Hong Huang, Jun Jie Alatancang,
Published in
Acta Mathematica Sinica, English Series

Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a ...

Zhou, Kai Jin, Lu
Published in
Acta Mathematica Sinica, English Series

This paper gives a generalization of the classical Borel’s Lemma. Then as an application of this generalized Borel’s Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of ℂm into ℙn(ℂ) (n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved.

Zhu, San Guo
Published in
Acta Mathematica Sinica, English Series

Let E be a Moran set on ℝ1 associated with a bounded closed interval J and two sequences (nk)k=1∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n_k)_{k=1}^\infty$$\en...

Wu, Chang Hui Wang, Zhi Jie Yu, Tao
Published in
Acta Mathematica Sinica, English Series

Let H2(γ) be the Hilbert space over the bidisk D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{D}^2$$\end{document} generated by a positive sequence γ = {γnm}...

Lim, Meng Fai

Let $p$ be an odd prime and $F_{\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group $G$. Suppose that $G$ is a compact pro-$p$ $p$-adic Lie group with no torsion and that it contains a closed normal subgroup $H$ such that $G/H\cong \mathbb{Z}_p$. Under various assumptions, we establish asymptotic upper bounds for the growth of...

Liu, Qing Yang
Published in
Acta Mathematica Sinica, English Series

Sarnak’s Disjointness Conjecture states that the Möbius function is disjoint with any zero-entropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimensional torus.