• 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.

• 대한수학회보
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• 제45권3호
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• pp.405-417
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• 2008

In this paper we prove some Hardy inequalities in the half space of the Heisenberg group and indicate the sharp constant.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.193-202
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• 2005

We define a general space $H_{{\omega},p}$ of the Hardy space and improve that Aleman's results to the space $H_{{\omega},p}$. It follows that the multiplication operator on this space is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.

• 대한수학회논문집
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• 제20권4호
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• pp.703-708
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• 2005

Let ${\varphi}(z)\;=\;({\varphi}_1(Z),{\cdots},{\varphi}_n(Z))$ be a holomorphic self­map of $\mathbb{D}^n$, where $\mathbb{D}^n$ is the unit polydisk of $\mathbb{C}^n$. The sufficient and necessary conditions for a composition operator to be bounded and compact from the Hardy space $H^2(\mathbb{D}^n)$ into $\alpha$-Bloch space $\beta^{\alpha}(\mathbb{D}^n)$ on the polydisk are given.

• 호남수학학술지
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• 제39권2호
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• pp.143-159
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• 2017

In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

• 대한수학회지
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• 제57권4호
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• pp.973-986
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• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• 대한수학회보
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• 제58권2호
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• pp.365-384
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• 2021

Let A be an expansive dilation on ℝn, and p(·) : ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. Let Hp(·)A (ℝn) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the author obtains the boundedness of anisotropic convolutional ��-type Calderón-Zygmund operators from Hp(·)A (ℝn) to Lp(·) (ℝn) or from Hp(·)A (ℝn) to itself. In addition, the author also obtains the duality between Hp(·)A (ℝn) and the anisotropic Campanato spaces with variable exponents.

• 호남수학학술지
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• 제45권1호
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• pp.71-81
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• 2023

In this paper, we deal with some geometric properties including starlikeness and convexity of order 𝛽 of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire functions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.125-130
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• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• 대한수학회논문집
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• 제21권4호
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• pp.631-640
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• 2006

In this paper, we prove sufficient conditions of boundedness of maximal operators on the p-adic vector space. We also consider weighted Hardy-Littlewood averages on the p-adic vector space.