• Journal of the Korean Mathematical Society
• /
• v.39 no.6
• /
• pp.899-912
• /
• 2002

In this paper, the boundedness of some commutators related to linear operators on weak Herz spaces are obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.1053-1066
• /
• 2024

In this paper, we study the boundedness of the commutator H^b_Ω formed by the rough Hardy operator H_Ω and a locally integrable function b from homogeneous Herz spaces to homogeneous weak Herz spaces. In addition, the weak boundedness of H^b_Ω on central Morrey spaces is also established.

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.33-69
• /
• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Kyungpook Mathematical Journal
• /
• v.64 no.2
• /
• pp.245-260
• /
• 2024

In this study, we establish some new characterizations for a class of anisotropic Herz spaces in which all exponents are considered as variables. We also provide a description of these spaces based on bloc decomposition. As an application, we investigate the boundedness of certain sublinear operators within these function spaces.

• Journal of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.829-842
• /
• 2012

In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of $\mathbb{C}^n$. And we provide the integral estimates concerning pluriharmonic kernel functions. Using this, we finally obtain the growth estimates of the Berezin transforms on such Herz spaces.

• 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.58 no.3
• /
• pp.767-779
• /
• 2021

Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.259-275
• /
• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.939-962
• /
• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Journal of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.713-732
• /
• 2017

Let ${\Omega}{\in}L^s(S^{n-1})$ for s > 1 be a homogeneous function of degree zero and b be BMO functions or Lipschitz functions. In this paper, we obtain some boundedness of the $Calder{\acute{o}}n$-Zygmund singular integral operator $T_{\Omega}$ and its commutator [b, $T_{\Omega}$] on Herz-type Hardy spaces with variable exponent.