Abstract : In this paper, we study the boundedness of a class of inhomogeneous Journ\'{e}'s product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journ\'{e}'s product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
Abstract : One says that a ring homomorphism $R \rightarrow S$ is \emph{Ohm-Rush} if extension commutes with arbitrary intersection of ideals, or equivalently if for any element $f\in S$, there is a unique smallest ideal of $R$ whose extension to $S$ contains $f$, called the \emph{content} of $f$. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically `yes' in dimension one, but `no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.
Abstract : Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. Let $\omega_A(T)$ and ${\|T\|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbert space $\big(\mathcal{H}, {\langle \cdot, \cdot\rangle}_A\big)$, respectively, where ${\langle x, y\rangle}_A := \langle Ax, y\rangle$ for all $x, y\in\mathcal{H}$. In this paper, we show with different techniques from that used by Kittaneh in \cite{FK} that \begin{equation*} \tfrac{1}{4}\|T^{\sharp_A} T+TT^{\sharp_A}\|_A\le \omega_A^2\left(T\right) \le \tfrac{1}{2}\|T^{\sharp_A} T+TT^{\sharp_A}\|_A. \end{equation*} Here $T^{\sharp_A}$ denotes a distinguished $A$-adjoint operator of $T$. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the $\mathbb{A}$-numerical radius of the operator matrix $\left(\begin{smallmatrix} I&T\\ 0&-I \end{smallmatrix}\right)$ where $\mathbb{A}= \text{diag}(A,A)$. In addition, several $A$-numerical radius inequalities for semi-Hilbert space operators are also established.
Abstract : By considering the polynomial function $\phi_{car}(z)=1+z+z^2/2,$ we define the class $\Scar$ consisting of normalized analytic functions $f$ such that $zf'/f$ is subordinate to $\phi_{car}$ in the unit disk. The inclusion relations and various radii constants associated with the class $\Scar$ and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.
Abstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]. Theorem 1 in the original paper has three assertions (i)-(iii), but we add (iv) after having clarified the argument.
Abstract : Let $G=(V,E)$ be a connected locally finite and weighted graph, $\Delta_p$ be the $p$-th graph Laplacian. Consider the $p$-th nonlinear equation $$-\Delta_pu+h|u|^{p-2}u=f(x,u)$$ on $G$, where $p>2$, $h,f$ satisfy certain assumptions. Grigor'yan-Lin-Yang \cite{GLY2} proved the existence of the solution to the above nonlinear equation in a bounded domain $\Omega\subset V$. In this paper, we show that there exists a strictly positive solution on the infinite set $V$ to the above nonlinear equation by modifying some conditions in \cite{GLY2}. To the $m$-order differential operator $\mathcal{L}_{m,p}$, we also prove the existence of the nontrivial solution to the analogous nonlinear equation.
Abstract : We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.
Abstract : Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the $q$-gamma, $q$-digamma and $q$-polygamma functions. More precisely, some classes of functions involving the $q$-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the $q$-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the $q$-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the $q$-digamma function and two-sided exponential bounding inequalities are then obtained for the $q$-tetragamma function.
Abstract : In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type \begin{equation*} u(x)=\overrightarrow{l}+C_{*}\int_{\mathbb{R}^n}\frac{(1-|u(y)|^2)|u(y)|^2u(y)-\frac{1}{2}(1-|u(y)|^2)^2u(y)}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:\mathbb{R}^n\rightarrow \mathbb{R}^k$ is a bounded, uniformly continuous function with $k\geqslant1$ and $0
Abstract : This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer $s\geq2$ and {$0\leq a
Sangwook Lee
J. Korean Math. Soc. 2022; 59(2): 421-438
https://doi.org/10.4134/JKMS.j210435
Jundong Zhou
J. Korean Math. Soc. 2022; 59(1): 53-69
https://doi.org/10.4134/JKMS.j200665
Li Zhu
J. Korean Math. Soc. 2022; 59(2): 407-420
https://doi.org/10.4134/JKMS.j210371
Hyunjin Lee, Young Jin Suh, Changhwa Woo
J. Korean Math. Soc. 2022; 59(2): 255-278
https://doi.org/10.4134/JKMS.j200614
Hyunjin Lee, Young Jin Suh, Changhwa Woo
J. Korean Math. Soc. 2022; 59(2): 255-278
https://doi.org/10.4134/JKMS.j200614
Xuan Yu
J. Korean Math. Soc. 2022; 59(1): 171-192
https://doi.org/10.4134/JKMS.j210271
Huabin Chen, Qunjia Wan
J. Korean Math. Soc. 2022; 59(2): 279-298
https://doi.org/10.4134/JKMS.j210111
Nak Eun Cho, Anbhu Swaminathan, Lateef Ahmad Wani
J. Korean Math. Soc. 2022; 59(2): 353-365
https://doi.org/10.4134/JKMS.j210246
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