• 제목/요약/키워드: Orlicz

검색결과 48건 처리시간 0.019초

PARAMETER MARCINKIEWICZ INTEGRAL AND ITS COMMUTATOR ON GENERALIZED ORLICZ-MORREY SPACES

  • Lu, Guanghui
    • 대한수학회지
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    • 제58권2호
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    • pp.383-400
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    • 2021
  • The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator ����Ω,b which is generated by the parameter Marcinkiwicz integral ����Ω and the Lipschitz function b on generalized Orlicz-Morrey space L��,��(Rd) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral ����Ω on the L��,��(Rd), and the commutator [b,����Ω] generated by the ����Ω and the space BMO on the L��,��(Rd), are also obtained, respectively.

ON PARANORMED TYPE p-ABSOLUTELY SUMMABLE UNCERTAIN SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS

  • Nath, Pankaj Kumar;Tripathy, Binod Chandra
    • 대한수학회논문집
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    • 제36권1호
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    • pp.121-134
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    • 2021
  • In this paper we introduce the notion of paranormed p-absolutely convergent and paranormed Cesro summable sequences of complex uncertain variables with respect to measure, mean, distribution etc. defined by on Orlicz function. We have established some relationships among these notions as well as with other classes of complex uncertain variables.

DIRICHLET EIGENVALUE PROBLEMS UNDER MUSIELAK-ORLICZ GROWTH

  • Benyaiche, Allami;Khlifi, Ismail
    • 대한수학회지
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    • 제59권6호
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    • pp.1139-1151
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    • 2022
  • This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝN and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS

  • Akgun Ramazan;Israfilov Daniyal M.
    • 대한수학회지
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    • 제43권2호
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    • pp.413-424
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    • 2006
  • Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

Some Difference Paranormed Sequence Spaces over n-normed Spaces Defined by a Musielak-Orlicz Function

  • Raj, Kuldip;Sharma, Sunil K.;Gupta, Amit
    • Kyungpook Mathematical Journal
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    • 제54권1호
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    • pp.73-86
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    • 2014
  • In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

THE ANALOGUE OF WIENER SPACE WITH VALUES IN ORLICZ SPACE

  • Ryu, Kun Sik
    • 충청수학회지
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    • 제27권4호
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    • pp.689-695
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    • 2014
  • Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

COHERENT AND CONVEX HEDGING ON ORLICZ HEARTS IN INCOMPLETE MARKETS

  • Kim, Ju-Hong
    • Journal of applied mathematics & informatics
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    • 제30권3_4호
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    • pp.413-428
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    • 2012
  • Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES

  • JIANG, ZHI-JIE
    • 대한수학회보
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    • 제52권4호
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    • pp.1383-1399
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    • 2015
  • Let ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ be the open unit disk in the complex plane $\mathbb{C}$, ${\varphi}$ an analytic self-map of $\mathbb{D}$ and ${\psi}$ an analytic function in $\mathbb{D}$. Let D be the differentiation operator and $W_{{\varphi},{\psi}}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{{\varphi},{\psi}}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\mathbb{D}$ are characterized.

On Some New Paranormed Difference Sequence Spaces Defined by Orlicz Functions

  • Tripathy, Binod Chandra;Dutta, Hemen
    • Kyungpook Mathematical Journal
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    • 제50권1호
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    • pp.59-69
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    • 2010
  • The main aim of this article is to introduce a new class of sequence spaces using the concept of n-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to derived (n-1)-norm. We use an Orlicz function, a bounded sequence of positive real numbers and some difference operators to construct these spaces so that they become more generalized and some other spaces can be derived under special cases. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces.