• Title/Summary/Keyword: integral operators

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COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES

  • Tong, Ce-Zhong;Zhou, Ze-Hua
    • Journal of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.125-135
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    • 2014
  • We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES

  • Shi, Yanlong;Tao, Xiangxing
    • 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.

SOME DECOMPOSITION FORMULAS ASSOCIATED WITH THE SARAN FUNCTION FE

  • Kim, Yong-Sup;Hasanov, Anvar;Lee, Chang-Hyun
    • Honam Mathematical Journal
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    • v.32 no.4
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    • pp.581-592
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    • 2010
  • With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function $F_E$ in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function $F_E$.

Fractional Integrals and Generalized Olsen Inequalities

  • Gunawan, Hendra;Eridani, Eridani
    • Kyungpook Mathematical Journal
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    • v.49 no.1
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    • pp.31-39
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    • 2009
  • Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

BEST RANDOM PROXIMITY PAIR THEOREMS FOR RELATIVELY U-CONTINUOUS RANDOM OPERATORS WITH APPLICATIONS

  • Okeke, Godwin Amechi
    • East Asian mathematical journal
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    • v.33 no.3
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    • pp.271-289
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    • 2017
  • It is our purpose in this paper to introduce the concept of best random proximity pair for subsets A and B of a separable Banach space E. We prove some best random approximation and best random proximity pair theorems of certain classes of random operators, which is the stochastic verse of the deterministic results of Eldred et al. [22], Eldred et al. [18] and Eldred and Veeramani [19]. Furthermore, our results generalize and extend recent results of Okeke and Abbas [42] and Okeke and Kim [43]. Moreover, we shall apply our results to study nonlinear stochastic integral equations of the Hammerstein type.

FRACTIONAL CALCULUS OPERATORS OF THE PRODUCT OF GENERALIZED MODIFIED BESSEL FUNCTION OF THE SECOND TYPE

  • Agarwal, Ritu;Kumar, Naveen;Parmar, Rakesh Kumar;Purohit, Sunil Dutt
    • Communications of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.557-573
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    • 2021
  • In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric 2F1(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.

CERTAIN IMAGE FORMULAS OF (p, 𝜈)-EXTENDED GAUSS' HYPERGEOMETRIC FUNCTION AND RELATED JACOBI TRANSFORMS

  • Chopra, Purnima;Gupta, Mamta;Modi, Kanak
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.1055-1072
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    • 2022
  • Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function Fp,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function Fp,𝜈(a, b; c; z) and Fox-Wright function rΨs(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function Fp,𝜈(a, b; c; z).

A simplified matrix stiffness method for analysis of composite and prestressed beams

  • Deretic-Stojanovic, Biljana;Kostic, Svetlana M.
    • Steel and Composite Structures
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    • v.24 no.1
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    • pp.53-63
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    • 2017
  • The paper presents the simplified matrix stiffness method for analysis of composite and prestressed beams. The method is based on the previously developed "exact" analysis method that uses the mathematical theory of linear integral operators to derive all relations without any mathematical simplifications besides inevitable idealizations related to the material rheological properties. However, the method is limited since the closed-form solution can be found only for specific forms of the concrete creep function. In this paper, the authors proposed the simplified analysis method by introducing the assumption that the unknown deformations change linearly with the concrete creep function. Adopting this assumption, the nonhomogeneous integral system of equations of the "exact" method simplifies to the system of algebraic equations that can be easily solved. Therefore, the proposed method is more suitable for practical applications. Its high level of accuracy in comparison to the "exact" method is preserved, which is illustrated on the numerical example. Also, it is more accurate than the well-known EM method.

WEIGHTED VECTOR-VALUED BOUNDS FOR A CLASS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS AND APPLICATIONS

  • Chen, Jiecheng;Hu, Guoen
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.671-694
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    • 2018
  • In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.745-758
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    • 2011
  • Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.