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

Samko, Stefan

http://hdl.handle.net/10400.1/16553

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Authors

Samko, Stefan

Abstract(s)

We 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).