• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.377-387
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• 2006

In this paper, we study the $L^p$ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to $L(log^+\;L)^2$. Our results extend as well as improve some known results on singular integrals.

• 대한수학회보
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• 제56권5호
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• pp.1099-1115
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• 2019

In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class ${\mathcal{F}}_{\beta}(S^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g^*_{\lambda}$-functions and area integrals are also presented.

• 대한수학회보
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• 제58권4호
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• pp.815-828
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• 2021

Under some mild conditions for the weight function K, the boundedness, compactness and essential norm of integral operators T_g and I_g from Morrey type spaces H^p_K to weighted BMOA spaces $BMOAK_{K,{\frac{2}{p}}}$ investigated in this paper.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.31-46
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• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• 충청수학회지
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• 제26권3호
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• pp.467-475
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• 2013

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

• East Asian mathematical journal
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• 제21권2호
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• 호남수학학술지
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• 제37권4호
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• pp.397-409
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• 2015

This paper considers a class of new convolution integral equations whose kernels involve special functions such as the generalized Mittag-Leffler function and the extended Kummer hypergeometric function. Some basic properties of interconnection with the familiar Riemann-Liouville operators are obtained which are used in fiding the solution of the main convolution integral equation. Several consequences are deduced from the main result by incorporating certain extended forms of hypergeometric functions in our present investigation.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.91-103
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• 2021

In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.