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BMO-VMO results for fractional integrals in variable exponent Morrey spaces
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We prove the boundedness of the fractional integration operator of variable order alpha(x) in the limiting Sobolev case alpha(x)p(x) = n - lambda(x) from variable exponent Morrey spaces L-p(.),L-lambda(.) (Omega) into BMO (Omega), where Omega is a bounded open set. In the case alpha(x) (math) const, we also show the boundedness from variable exponent vanishing Morrey spaces VLp(.),lambda (.) (Omega) into VMO (Omega). The results seem to be new even when p and A are constant. (C) 2019 Elsevier Ltd. All rights reserved.
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Pergamon-Elsevier Science Ltd