Guliyev Vagif S, Deringoz Fatih, Hasanov Sabir G
Department of Mathematics, Ahi Evran University, Kirsehir, Turkey.
S.M. Nikol'skii Institute of Mathematics, RUDN University, 6 Miklukho-Maklay St, Moscow, 117198 Russia.
J Inequal Appl. 2017;2017(1):75. doi: 10.1186/s13660-017-1349-4. Epub 2017 Apr 13.
In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator [Formula: see text] on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1):247-286, 2011) found necessary and sufficient conditions on general Young functions Φ and Ψ ensuring that this operator is of weak or strong type from [Formula: see text] into [Formula: see text]. Our characterizations for the boundedness of the above-mentioned operator are different from the ones in (Cianchi in J. Lond. Math. Soc. 60(1):247-286, 2011). As an application of these results, we consider the boundedness of the commutators of Riesz potential operator [Formula: see text] on Orlicz spaces when belongs to the BMO and Lipschitz spaces, respectively.
在本文中，我们将给出里斯位势算子[公式：见正文]在奥利奇空间上强有界性和弱有界性的充分必要条件。钱奇（《伦敦数学会杂志》60(1):247 - 286, 2011）找到了关于一般杨函数Φ和Ψ的充分必要条件，确保该算子从[公式：见正文]到[公式：见正文]是弱型或强型的。我们对上述算子有界性的刻画与（钱奇，《伦敦数学会杂志》60(1):247 - 286, 2011）中的不同。作为这些结果的一个应用，我们分别考虑当属于BMO和利普希茨空间时，里斯位势算子[公式：见正文]在奥利奇空间上的交换子的有界性。
