• Title/Summary/Keyword: integral operators

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CONVEXITY OF INTEGRAL OPERATORS GENERATED BY SOME NEW INEQUALITIES OF HYPER-BESSEL FUNCTIONS

  • Din, Muhey U.
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1163-1173
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    • 2019
  • In this article, we deduced some new inequalities related to hyper-Bessel function. By using these inequalities we will find some sufficient conditions under which certain families of integral operators are convex in the open unit disc. Some applications related to these results are also the part of our investigation.

WEIGHTED ESTIMATES FOR ROUGH PARAMETRIC MARCINKIEWICZ INTEGRALS

  • Al-Qassem, Hussain Mohammed
    • Journal of the Korean Mathematical Society
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    • v.44 no.6
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    • pp.1255-1266
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    • 2007
  • We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\mathcal{M}^{\rho}_{\Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}$ related to the Littlewood-Paley $g^*_{\lambda}-function$ and the area integral S, respectively.

EVALUATION FORMULA FOR WIENER INTEGRAL OF POLYNOMIALS IN TERMS OF NATURAL DUAL PAIRINGS ON ABSTRACT WIENER SPACES

  • Chang, Seung Jun;Choi, Jae Gil
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1093-1103
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    • 2022
  • In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces (H, B, 𝜈). To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in 𝓛(B), the Banach space of bounded linear operators from B to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in 𝓛(B). We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.

BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON INHOMOGENEOUS PRODUCT LIPSCHITZ SPACES

  • He, Shaoyong;Zheng, Taotao
    • Journal of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.469-494
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    • 2022
  • In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

SUFFICIENT CONDITIONS FOR UNIVALENCE OF A GENERAL INTEGRAL OPERATOR

  • Selvaraj, Chellian;Karthikeyan, Kadhavoor Ragavan
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.367-372
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    • 2009
  • In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.

SOME NEW INTEGRAL MEANS INEQUALITIES AND INCLUSION PROPERTIES FOR A CLASS OF ANALYTIC FUNCTIONS INVOLVING CERTAIN INTEGRAL OPERATORS

  • Raina, R.K.;Bansal, Deepak
    • East Asian mathematical journal
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    • v.24 no.4
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    • pp.347-358
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    • 2008
  • In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.

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