• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.937-958
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• 1996

On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.141-149
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• 2011

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We show that Toeplitz operators induced by elements of some set are bounded and each element of the set is related with a Carleson measure on the weighted Bergman space.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.349-369
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• 2013

The present paper envisages the $q$-analogue of the exponential operators, determined by G. Dattoli and his collaborators for translation and diffusive operators which were utilized to establish analytical solutions of difference and integral equations. The generalization of their technique is expected to cover wide range of such utilization.

• Journal of the Korean Mathematical Society
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• v.6 no.2
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• pp.55-73
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• 1969

• Honam Mathematical Journal
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• v.7 no.1
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• pp.1-6
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• 1985

Bounded linear operators defined from a space with vector norm into (LF)-complete vector lattice are represented by Hellinger integration.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.127-145
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• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1801-1816
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• 2017

We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol g on the Fock-Sobolev spaces ${\mathcal{F}}^p_{{\psi}m}$. We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ if and only if g is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of g being not bigger than one. We also identified all those positive numbers p for which the operator $V_g$ belongs to the Schatten $S_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of g.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.297-308
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• 2002

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.