Orlicz-fractional maximal operators on weighted Lp spaces

Necessary and sufficient conditions for weight norm inequalities on Lebesgue spaces to hold are given in the scale of Orlicz spaces for the fractional Orlicz maximal operators which generalizes the fractional maximal operators. A similar argument for the Orlicz maximal operators is due to Pérez, who generalizes for the Fefferman-Stein inequality. The main result is the Fefferman-Stein inequality for the fractional maximal operators of the Sawyer type and the Hardy-Littlewood-Sobolev type. In this paper, we establish that the Lp -boundedness and the Fefferman-Stein type inequality of Orlicz maximal operator are essentially equivalent to the Saywer type inequality for the fractional Orlicz maximal operators. These inequalities are stronger than the Hardy-Littlewood-Sobolev type inequalities. More generally, we consider several mixed strong type inequalities for the ordinary and generalized fractional Orlicz maximal operators. As an application, we investigate the weight norm inequalities of the commutator [b, Iα], where b ∈ BMO(ℝn), and Iα the fractional integral operator. © Element, Zagreb.

Authors
Iida T.1 , Sawano Y. 2, 3
Publisher
Element D.O.O.
Number of issue
2
Language
English
Pages
369-413
Status
Published
Volume
13
Year
2019
Organizations
  • 1 Department of General Education, National Institute of Technology, Fukushima College, Nagao 30, Kamiarakawa-az, Tairaa, Iwaki-city, Fukushima-Ken, 970-8034, Japan
  • 2 Department of Mathematics and Information Science, Tokyo Metropolitan University, Minamioosawa 1-1, Hachouji-city, Tokyo, 192-0364, Japan
  • 3 Department of Mathematics Analysis and the Theory of functions, Peoples' Friendship University of Russia, Moscow, Russian Federation
Keywords
Commutator; Fractional integral operator; Fractional Orlicz maximal operator; Orlicz maximal operator; Weight
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38601/
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