Fractional Integrals and Generalized Olsen Inequalities

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 1,  2009, pp.31-39
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.1.031
Title & Authors
Fractional Integrals and Generalized Olsen Inequalities
Gunawan, Hendra; Eridani, Eridani;

Abstract
Let $\small{T_{\rho}}$ be the generalized fractional integral operator associated to a function $\small{{\rho}:(0,{\infty}){\rightarrow}(0,{\infty})}$, as defined in [16]. For a function W on $\small{\mathbb{R}^n}$, we shall be interested in the boundedness of the multiplication operator $\small{f{\mapsto}W{\cdot}T_{\rho}f}$ on generalized Morrey spaces. Under some assumptions on $\small{{\rho}}$, we obtain an inequality for $\small{W{\cdot}T_{\rho}}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.
Keywords
Fractional integral operators;Hardy-Littlewood maximal operators;multiplication operators;Olsen inequality;Morrey spaces;
Language
English
Cited by
1.
Weighted Hardy and potential operators in the generalized Morrey spaces, Journal of Mathematical Analysis and Applications, 2011, 377, 2, 792
2.
FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES, Bulletin of the Australian Mathematical Society, 2009, 80, 02, 324
3.
Generalized fractional integrals on generalized Morrey spaces, Mathematische Nachrichten, 2014, 287, 2-3, 339
4.
Boundedness for the commutator of fractional integral on generalized morrey space in nonhomogeneous space, Analysis in Theory and Applications, 2011, 27, 1, 51
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