Weighted adams type theorem for the riesz fractional integral in generalized morrey space

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Evgeniya Burtseva ◽  
Natasha Samko
Keyword(s):  
Fractional Integral ◽  
Morrey Space ◽  
Fractional Integration ◽  
Type Theorem ◽  
Integration Operator ◽  
Generalized Morrey Space ◽  
Fractional Integration Operator

AbstractWe prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Stefan Samko
Keyword(s):  
Fractional Integration ◽  
Fractional Integrals ◽  
Variable Order ◽  
Integration Operator ◽  
Hölder Continuous ◽  
Open Set ◽  
Fractional Integration Operator ◽  
Limiting Case

AbstractWe show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝn in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small order.

scholarly journals Fractional integration operator of variable order in the holder spacesHλ(x)

1995 ◽  
Vol 18 (4) ◽  
pp. 777-788 ◽  
Author(s):  
Bertram Ross ◽  
Stefan Samko
Keyword(s):  
Fractional Integration ◽  
Fractional Integrals ◽  
Variable Order ◽  
Integration Operator ◽  
Fractional Integration Operator ◽  
Type Spaces ◽  
Littlewood Theorem

The fractional integralsIa+α(x)φof variable orderα(x)are considered. A theorem on mapping properties ofIa+α(x)φin Holder-type spacesHλ(x)is proved, this being a generalization of the well known Hardy-Littlewood theorem.

scholarly journals On the boundedness of a generalized fractional integral on generalized Morrey spaces

2002 ◽  
Vol 33 (4) ◽  
pp. 335-340
Author(s):  
Eridani Eridani
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Campanato Space ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Generalized Fractional Integral

In this paper we extend Nakai's result on the boundedness of a generalized fractional integral operator from a generalized Morrey space to another generalized Morrey or Campanato space.

scholarly journals Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 1000-1014
Author(s):  
Suixin He ◽  
◽  
Shuangping Tao
Keyword(s):  
Bounded Domain ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Homogeneous Spaces ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Generalized Morrey Space ◽  
Fractional Integral Operators ◽  
Littlewood Maximal Operator

<abstract><p>The aim of this paper is to obtain the boundedness of some operator on grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ over non-homogeneous spaces, where $ G\subset $ $ \mathbb{R}^{n} $ is a bounded domain. Under assumption that functions $ \varphi $ and $ \phi $ satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and $ \theta $-type Calderón-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $. Moreover, the boundedness of commutator $ [b, T^{G}_{\theta}] $ which is generated by $ \theta $-type Calderón-Zygmund operator $ T_{\theta} $ and $ b\in\mathrm{RBMO}(\mu) $ on spaces $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ is also established.</p></abstract>

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