Variable exponent fractional integrals in the limiting case alpha(x)p(x) equivalent to n on quasimetric measure spaces

Samko, Stefan2021-06-242021-06-242020-031072-947Xhttp://hdl.handle.net/10400.1/16553We show that the fractional operator I-alpha(center dot), of variable order on a bounded open set in Omega, in a quasimetric measure space (X, d, mu) in the case alpha(x)p(x) = n (where n comes from the growth condition on the measure mu), is bounded from the variable exponent Lebesgue space L-p(center dot)(Omega) into BMO(Omega) under certain assumptions on p(x) and alpha(x).engRiesz potentialVariable exponent spacesSobolev type theoremBMO resultsQuasimetric measure spaceMathematicsVariable exponent fractional integrals in the limiting case alpha(x)p(x) equivalent to n on quasimetric measure spacesjournal article10.1515/gmj-2018-0047