Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 207-223, 2019


Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces

Daiki Hashimoto, Takao Ohno, Tetsu Shimomura

Received May 26, 2017.   Published online August 6, 2018.

Abstract:  We are concerned with the boundedness of generalized fractional integral operators $I_{\rho,\tau}$ from Orlicz spaces $L^{\Phi}(X)$ near $L^1(X)$ to Orlicz spaces $L^{\Psi}(X)$ over metric measure spaces equipped with lower Ahlfors $Q$-regular measures, where $\Phi$ is a function of the form $\Phi(r)=r\ell(r)$ and $\ell$ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.
Keywords:  Orlicz space; Riesz potential; fractional integral; metric measure space; lower Ahlfors regular
Classification MSC:  31B15, 46E30, 46E35
DOI:  10.21136/CMJ.2018.0258-17


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Affiliations:   Daiki Hashimoto, Nagasakihokuyodai High School, Nagasaki 851-2127, Japan; Takao Ohno, Faculty of Education, Oita University, Dannoharu Oita-city 870-1192, Japan, e-mail: t-ohno@oita-u.ac.jp; Tetsu Shimomura, Department of Mathematics, Graduate School of Education, Hiroshima University, 1-1-1, Kagamiyama, Higashi-Hiroshima 739-8524, Japan, e-mail: tshimo@hiroshima-u.ac.jp


 
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