• Bulletin of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.1391-1408
• /
• 2023

Let M and M^# be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators [M, b] and [M^#, b] in a general context of Banach function spaces when b belongs to BMO(?ⁿ) spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak-Orlicz spaces are also given.

• Korean Journal of Mathematics
• /
• v.11 no.2
• /
• pp.85-91
• /
• 2003

On the setting of the upper half-space of the euclidean space $\mathbf{R}^n$, we show some properties of weighted harmonic Bergman functions.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1187-1193
• /
• 2014

We will characterize the boundedness and compactness of weighted composition operators on the minimal M$\ddot{o}$bius invariant space.

• East Asian mathematical journal
• /
• v.38 no.1
• /
• pp.129-141
• /
• 2022

We obtain interior regularity estimates in the weighted Orlicz spaces for viscosity solutions of fully nonlinear uniformly parabolic equations u_t - F(D² u, x, t) = f(x, t) in Q₁ under relaxed structure conditions on the nonlinear operator F.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.439-454
• /
• 2014

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1277-1288
• /
• 2013

Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.187-198
• /
• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.467-475
• /
• 2013

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

• East Asian mathematical journal
• /
• v.19 no.1
• /
• pp.73-80
• /
• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• Journal of the Chungcheong Mathematical Society
• /
• v.14 no.2
• /
• pp.37-46
• /
• 2001

In this paper, weighted Bloch spaces $\mathcal{B}_q$ are considered on the open unit ball in $\mathbb{C}^n$. In this paper, we will show that every Bloch function in $B_q$ induces a bounded linear functional on $L^1_a(\mathcal{B})$.