• 대한수학회지
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• 제39권6호
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• pp.899-912
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• 2002

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

• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.253-265
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• 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.

• 대한수학회지
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• 제49권4호
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• pp.829-842
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• 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.

• 대한수학회보
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• 제58권3호
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• pp.767-779
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• 2021

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

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.315-328
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• 2006

In this paper, the Boundedness for the multilinear Littlewood-Paley operator on certain Hardy and Herz-Hardy spaces are obtained.

• 대한수학회지
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• 제39권3호
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• 대한수학회지
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• 제40권1호
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• pp.41-60
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• 2003

In this paper, the continuity for the commutators of Littlewood-Paley operators on certain Hardy and Herz-Hardy spaces are obtained.

• 대한수학회지
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• 제54권3호
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• pp.713-732
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• 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.

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.245-260
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• 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.

• 대한수학회보
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• 제51권2호
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.