• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.905-915
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• 2022

This paper studies the boundedness of integral operators on the Cesàro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erdélyi-Kober fractional integrals and the Mellin fractional integrals on the Cesàro function spaces.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.851-864
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• 2015

In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized g-function, Lusin area function and $g^*_{\lambda}$-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from BMO($\mathbb{R}^n$) to BLO($\mathbb{R}^n$), which improve and generalize some previous results.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.127-146
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• 2004

We give an extensive presentation of results about the properties of Banach space operators with weakly precompact adjoints. Further we give a description of operators having weakly precompact adjoints on abstract continuous function spaces.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.901-910
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• 2008

For some generalized N-function ${\Phi}$, some Holder type inequalities and bounded operators on spaces of type $W_M^{\Omega,\Phi}$ generalizing the $W^p$-spaces due to Pathak and Upadhyay are obtained.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.907-925
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• 2012

In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\acute{o}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

• Kyungpook Mathematical Journal
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• v.47 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.567-578
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• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

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