• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.53-62
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• 2004

A result of Hardy and Littlewood relates Holder continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. We call it the Hardy-Littlewood property. Langmeyer further extended their result to the class of John disks in terms of the inner length metric. We call it the Hardy-Littlewood property with the inner length metric. In this paper we give several properties of a domain which satisfies the Hardy-Littlewood property with the inner length metric. Also we show some results on the Holder continuity of conjugate harmonic functions in various domains.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1035-1049
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• 2023

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z^(𝜔)_r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.

• East Asian mathematical journal
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• v.34 no.5
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• pp.577-585
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• 2018

For the purpose of characterizing subharmonic or ${\mathcal{M}}$-subharmonic Hardy classes in the unit ball of ${\mathbb{C}}^n$, we establish fundamental identities between integral means in terms of volume integrals and Green's functions.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.395-410
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• 2006

We characterize the class of uniformly John domains in terms of the quasihyperbolic metric and from the result we get some analogues of the Hardy-Littlewood property for ${\alpha} = 0$ in uniformly John domains.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1221-1228
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• 2017

We consider weighted Hardy spaces on bidisk ${\mathbb{D}}^2$ which generalize the weighted Bergman spaces $A^2_{\alpha}({\mathbb{D}}^2)$. Let z, w be coordinate functions and $T_{{\bar{z}}^N}_w$ Toeplitz operator with symbol $_{{\bar{z}}^N}_w$. In this paper, we study the reducing subspaces of $T_{{\bar{z}}^N}_w$ on the weighted Hardy spaces.

• Honam Mathematical Journal
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• v.45 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.139-175
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• 2000

We consider the boundary behavior of a Hardy class holomorphic function, either on the disk D in the complex plane or on a domain in multi-dimensional complex space. Although the two theories are formally different, we postulate some unifying fearures, and we suggest some future directions for research.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.489-495
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• 2020

We define new integral operators on the Haydy space similar to Szegö projection. We consider a relationship between these Szegö type operators and the partial sum of Taylor series on the Hardy space.

• East Asian mathematical journal
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• v.19 no.2
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• pp.291-303
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• 2003

A result of Hardy and Littlewood relates Holder continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. In this paper we obtain a similar result to the class of uniformly John domains in terms of the inner diameter metric. We give several properties of a domain with the property. Also we show some results on the Holder continuity of conjugate harmonic functions in the above domains.

• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.