Jongrak Lee
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View article: Hyponormality of Toeplitz operators on Newton spaces
Hyponormality of Toeplitz operators on Newton spaces Open
In this paper, we investigate properties of hyponormal Toeplitz operators whose symbols are analytic or co-analytic on a Newton space. We establish both necessary and sufficient conditions for a Toeplitz operator $$T_{\varphi }$$ to be…
View article: Toeplitz operators on some function spaces
Toeplitz operators on some function spaces Open
We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of …
View article: Remarks on hyponormal Toeplitz operators with nonharmonic symbols
Remarks on hyponormal Toeplitz operators with nonharmonic symbols Open
In this article, we present some necessary or sufficient conditions for the hyponormality of Toeplitz operator T φ {T}_{\varphi } on the Bergman space A 2 ( D ) {A}^{2}\left({\mathbb{D}}) . In particular, we consider th…
View article: Complex symmetric Toeplitz operators on the generalized derivative Hardy space
Complex symmetric Toeplitz operators on the generalized derivative Hardy space Open
The generalized derivative Hardy space $S^{2}_{\alpha ,\beta}(\mathbb{D})$ consists of all functions whose derivatives are in the Hardy and Bergman spaces as follows: for positive integers α , β , $$ S^{2}_{\alpha ,\beta}(\mathb…
View article: Metapopulation of Ellobium chinense through the Late-middle and Late Pleistocene expansions: four covariate COI hotspots linked to G-quadruplex conformation
Metapopulation of Ellobium chinense through the Late-middle and Late Pleistocene expansions: four covariate COI hotspots linked to G-quadruplex conformation Open
The land snail Ellobium chinense (Pulmonata, Ellobiida, Ellobiidae), which inhabits the salt marshes along the coastal areas of northwestern Pacific, is an endangered species on the IUCN Red List. Over recent decades, the population size o…
View article: On multiple solutions to a nonlocal fractional $p(\cdot )$-Laplacian problem with concave–convex nonlinearities
On multiple solutions to a nonlocal fractional $p(\cdot )$-Laplacian problem with concave–convex nonlinearities Open
The aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional $p(\cdot )$ -Laplacian with concave–convex nonlinearities when, in general…
View article: Contractivity and expansivity of H-Toeplitz operators on the Bergman spaces
Contractivity and expansivity of H-Toeplitz operators on the Bergman spaces Open
In this paper we consider the properties of H-Toeplitz operators $ B_{\varphi} $ on the Bergman space $ L^2_a(\Bbb D) $. We present some necessary and sufficient conditions for the contractive and expansive H-Toeplitz operators $ B_\varphi…
View article: Metapopulation of Ellobium Chinense Through The Late-Middle and Late Pleistocene Expansions: Four Covariate COI Hotspots Linked to G-Quadruplex Conformation
Metapopulation of Ellobium Chinense Through The Late-Middle and Late Pleistocene Expansions: Four Covariate COI Hotspots Linked to G-Quadruplex Conformation Open
The land snail Ellobium chinense (Pulmonata, Ellobiida, Ellobiidae), which inhabits the salt marshes along the coastal areas of northwestern Pacific, is an endangered species on the IUCN Red List. Over recent decades, the population size o…
View article: Normal Toeplitz Operators on the Fock Spaces
Normal Toeplitz Operators on the Fock Spaces Open
We characterize normal Toeplitz operator on the Fock spaces F2(C). First, we state basic properties for Toeplitz operator Tφ on F2(C). Next, we study the normal Toeplitz operator Tφ on F2(C) in terms of harmonic symbols φ. Finally, we char…
View article: Normal Toeplitz Operators on the Bergman Space
Normal Toeplitz Operators on the Bergman Space Open
In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in te…
View article: Multiple solutions for polyharmonic equations with potential vanishing at infinity
Multiple solutions for polyharmonic equations with potential vanishing at infinity Open
We are concerned with the following polyharmonic equation: \begin{equation*} \Delta_p^L u+V(x)|u|^{p-2}u = K(x)f(x,u) and u>0 in \Bbb R^N, \end{equation*} where $1< p<\infty$, $N>Lp$, $L=1,2,\cdots$ and the potential functions $V, K:\Bbb R…
View article: Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN
Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN Open
We are concerned with the following elliptic equations: ( − Δ ) p , K s u + V ( x ) | u | p − 2 u = λ f ( x , u ) in R N , where ( − Δ ) p , K s is the nonlocal integrodifferential equation with 0 < s < 1 < p < + ∞ , s p < N the potential …
View article: m-Isometric block Toeplitz operators
m-Isometric block Toeplitz operators Open
In this paper, we study m-isometric block Toeplitz operators with trigonometric symbols. In addition, we give a necessary and sufficient condition for block Toeplitz operators with trigonometric polynomial symbols to be m-contractive.
View article: Multiplicity of Small or Large Energy Solutions for Kirchhoff–Schrödinger-Type Equations Involving the Fractional p-Laplacian in ℝN
Multiplicity of Small or Large Energy Solutions for Kirchhoff–Schrödinger-Type Equations Involving the Fractional p-Laplacian in ℝN Open
We herein discuss the following elliptic equations: M ∫ R N ∫ R N | u ( x ) − u ( y ) | p | x − y | N + p s d x d y ( − Δ ) p s u + V ( x ) | u | p − 2 u = λ f ( x , u ) in R N , where ( − Δ ) p s is the fractional p-Laplacian defined by (…
View article: Existence of nontrivial weak solutions for a quasilinear Choquard equation
Existence of nontrivial weak solutions for a quasilinear Choquard equation Open
We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text], [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see t…
View article: The existence of infinitely many solutions for nonlinear elliptic equations involving p-Laplace type operators in R^N
The existence of infinitely many solutions for nonlinear elliptic equations involving p-Laplace type operators in R^N Open
We are concerned with the following nonlinear elliptic equationswhere the function ϕ(x, v) is of type |v| p-2 v, b : R N → (0, ∞) is a continuous potential function, λ is a real parameter, and f : R N × R → R is a Carathéodory function.In …
View article: Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators
Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators Open
We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations $$ \textstyle\begin{cases} {-}\operatorname{div}(\varphi(x,\nabla u))+{|u|}^{p-2}u= \lambda f(x,u) &\mbox{in } \Omega,\\ \varph…
View article: A subnormal Toeplitz completion
A subnormal Toeplitz completion Open
In this paper we deal with a subnormal Toeplitz completion problem: Complete the unspecified Toeplitz operators of the partial block Toeplitz matrixto make G subnormal, where U is the shift on the Hardy space H 2 (T) of the unit circle T .