• Kyungpook Mathematical Journal
• /
• v.60 no.1
• /
• pp.117-125
• /
• 2020

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.427-430
• /
• 2009

In this paper we introduce the intermediate differential of a Lipschitz map from a Banach space to another Banach space and prove that every locally Lipschitz function f defined on an open subset ${\Omega}$ of a superreflexive real Banach space X to a finite dimensional Banach space Y is uniformly intermediate differentiable at every point ${\Omega}/A$, where A is a ${\sigma}$-lower porous set.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.931-940
• /
• 2007

Holomorphic mean Lipschitz space is defined in the unit ball of $\mathbb{C}^n$. The membership of the space is expressed in terms of the growth of radial derivatives, which reduced to a classical result of Hardy and Littlewood when n = 1. The membership is also expressed in terms of the growth of tangential derivatives when $n{\ge}2$.

• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.253-265
• /
• 2007

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1109-1124
• /
• 2018

For a metric space (X, d) and ${\alpha}$ > 0. We study the structure and properties of vector-valued Lipschitz algebra $Lip{\alpha}(X,E)$ and $lip{\alpha}(X,E)$ of order ${\alpha}$. We investigate the approximate and Character amenability of vector-valued Lipschitz algebras.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.469-494
• /
• 2022

In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé'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.

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.187-195
• /
• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.73-79
• /
• 2012

It is well-known that the BMO norm is equivalent to the Garsia norm. In this paper, we characterize mean-Lipschitz spaces by using Garsia-type norms on the upper half space $\mathbb{R}_+^{n+1}$.

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.819-825
• /
• 2016

In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.805-821
• /
• 2000

The paper deals with asymtotic stabillity of nonlinear nonautinomous systems by Lyapunov's direct method. The proposed Lyapunov-like function V(t, x) needs not be continuous in t and Lipschitz in x in a Banach space. The class of systems considered is allowed to be nonautonomous and infinite-dimensional and we relax the boundedness, the Lipschitz assumption on the system and the definite decrescent condition on the Lyapunov function.