Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L1 Over Metric Measure Spaces
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We are concerned with the boundedness of generalized fractional integral operators Iϱ,τ from Orlicz spaces LΦ(X) near L1(X) to Orlicz spaces LΨ(X) over metric measure spaces equipped with lower Ahlfors Q-regular measures, where Φ is a function of the form Φ(r) = rl(r) and l 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.
KeywordsOrlicz space Riesz potential fractional integral metric measure space lower Ahlfors regular
MSC 201031B15 46E30 46E35
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