Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz--Morrey spaces of the third kind

2018/12/10 by Deringoz, Fatih, Guliyev, Vagif S., Nakai, Eiichi +2 · 1 citation
#42B20 #42B25 #42B35 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1812.03649

Abstract

In the present paper, we will characterize the boundedness of the generalized fractional integral operators I_ρ and the generalized fractional maximal operators M_ρ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators M_ρ and I_ρ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators M_ρ and I_ρ on generalized Orlicz--Morrey spaces.

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• New weighted Riesz-type pointwise inequalities and applications to generalized Sobolev estimates

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