Criteria for the Boundedness of Potential Operators in Grand Lebesgue Spaces

Mathematics – Functional Analysis

Scientific paper

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15 pages

Scientific paper

It is shown that that the fractional integral operators with the parameter $\alpha$, $0<\alpha<1$, are not bounded between the generalized grand Lebesgue spaces $L^{p), \theta_1}$ and $L^{q), \theta_2}$ for $\theta_2 < (1+\alpha q)\theta_1$, where $1

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