A note on Riesz fractional integrals in the limiting case alpha(x)p(x) a parts per thousand n

Samko, Stefan2018-12-072018-12-072013-061311-0454http://hdl.handle.net/10400.1/11563We show that the Riesz fractional integration operator I (alpha(center dot)) of variable order on a bounded open set in Omega aS, a"e (n) in the limiting Sobolev case is bounded from L (p(center dot))(Omega) into BMO(Omega), if p(x) satisfies the standard logcondition and alpha(x) is Holder continuous of an arbitrarily small order.engLebesgue spacesVariable exponentOperatorsConvolutionA note on Riesz fractional integrals in the limiting case alpha(x)p(x) a parts per thousand njournal article10.2478/s13540-013-0023-x