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HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES
( Jongrak Lee ),( Youho Lee ) 호남수학회 2013 호남수학학술지 Vol.35 No.2
In this note we consider the hyponormality of Toeplitz operators T%, on the Weighted Bergman space A2α(D) with symbol in the class of functions f +g with polynomials f and g of degree
HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES
Lee, Jongrak,Lee, Youho The Honam Mathematical Society 2013 호남수학학술지 Vol.35 No.2
In this note we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ with symbol in the class of functions $f+\bar{g}$ with polynomials $f$ and $g$ of degree 2.
HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
Lee, Jongrak The Kangwon-Kyungki Mathematical Society 2007 한국수학논문집 Vol.15 No.2
In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a({\mathbb{D})$ with symbol in the case of function $f+{\overline{g}}$ with polynomials $f$ and $g$. We present some necessary conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.
Existence of nontrivial weak solutions for a quasilinear Choquard equation
Lee, Jongrak,Kim, Jae-Myoung,Bae, Jung-Hyun,Park, Kisoeb Springer International Publishing 2018 Journal of inequalities and applications Vol.2018 No.1
<P>We are concerned with the following quasilinear Choquard equation: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ -\Delta_{p} u+V(x)|u|^{p-2}u=\lambda\bigl(I_{\alpha} \ast F(u)\bigr)f(u) \quad \text{in } \mathbb {R}^{N}, \qquad F(t)= \int_{0}^{t}f(s) \,ds, $$\end{document}−<SUB>Δp</SUB>u+V(x)<SUP>|u|p−2</SUP>u=λ(<SUB>Iα</SUB>∗F(u))f(u)in <SUP>RN</SUP>,F(t)=∫0tf(s)ds, where [FORMULA OMISSION], [FORMULA OMISSION] is the <I>p</I>-Laplacian operator, the potential function [FORMULA OMISSION] is continuous and [FORMULA OMISSION]. Here, [FORMULA OMISSION] is the Riesz potential of order [FORMULA OMISSION]. We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term <I>f</I>.</P>
New Records of Two Dendronotid Nudibranchs from Korea
Jongrak Lee,Hyun Jong Kil,Sa Heung Kim 한국동물분류학회 2020 Animal Systematics, Evolution and Diversity Vol.36 No.4
Two cold water species of dendronotid nudibranchs are described for the first time in Korea: Dendronotus frondosus (Ascanius, 1774) and Dendronotus robilliardi Korshunova, Sanamyan, Zimina, Fletcher & Martynov, 2016. Dendronotus frondosus is characterized by the color pattern of deep dark-brown with white specks and mottles on the dorsum. Dendronotus robilliardi is distinguished by the body of translucent white with milky stripes and orange-brown markings in papillae, and D. robilliardi from Korean water is commonly examined with white dots on the anterior dorsum. Images of external morphology and brief re-descriptions of two species were provided. Further, we confirmed the opinion of Korshunova et al. that the Korean D. albus image by Koh would be D. robilliardi.