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Estimates for the variable order Riesz potential with applications
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Estimates for the variable order Riesz potential with applications
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We study weak-type estimates and exponential integrability for the variable order Riesz potential. As an application we prove an exponential integrability result with respect to the Hausdorff content for functions from variable exponent Sobolev spaces. In particular, the earlier exponential integrability results are improved to a corresponding one with respect to the Choque integral whenever John domains are considered. Moreover, new exponential integrability results also for domains with outward cusps are obtained.
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Cited by 1 Pith paper
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Bounds for the maximal and Riesz potential operators with variable fractionality
Proves L^{p(·)}-to-L^{q(·)} bounds for variable fractional maximal and Riesz potential operators under three-exponent Muckenhoupt conditions using adapted sparse domination.
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