Geodesic
Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 207-223

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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.
DOI : 10.21136/CMJ.2018.0258-17
Classification : 31B15, 46E30, 46E35
Keywords: Orlicz space; Riesz potential; fractional integral; metric measure space; lower Ahlfors regular 
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Hashimoto, Daiki; Ohno, Takao; Shimomura, Tetsu. Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 207-223. doi: 10.21136/CMJ.2018.0258-17

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