• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.403-417
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• 2021

This note is devoted to establishing the boundedness for some classes of Littlewood-Paley square operators defined by the kernels without any regularity on the mixed radial-angular spaces. The corresponding vector-valued versions are also presented. As applications, the corresponding results for the Littlewood-Paley g∗λ function and the Littlewood-Paley function related to the area integrals are also obtained.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.152-166
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• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1073-1087
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• 2022

We introduce two new classes of lightlike submersions, namely, screen slant and screen semi-slant lightlike submersions from an indefinite Kaehler manifold to a lightlike manifold giving characterization theorems with non trivial examples for both classes. Integrability conditions of all distributions related to the definitions of these submersions have been obtained.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.801-810
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• 2022

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.701-715
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• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.277-291
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• 2022

The aim of this article is to examine some types of slant submanifolds of bronze Riemannian manifolds. We introduce hemi-slant submanifolds of a bronze Riemannian manifold. We obtain integrability conditions for the distribution involved in quasi hemi-slant submanifold of a bronze Riemannian manifold. Also, we give some examples about this type submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1409-1425
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• 2023

In this paper, we are devoted to studying the mixed radial-angular integrabilities for Hardy type operators. As an application, the upper and lower bounds are obtained for the fractional Hardy operator. In addition, we also establish the sharp weak-type estimate for the fractional Hardy operator.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.835-844
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• 2010

In this paper we study the $H{\grave{a}}jeck-R{\grave{e}}nyi$ type inequality and strong law of large numbers for asymptotically quadrant sub-independent(AQSI) sequences. We also prove the integrability of supremum for AQSI sequences.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.248-268
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• 2023

As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.

• Kyungpook Mathematical Journal
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• v.64 no.1
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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.