A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n
A note on Riesz fractional integrals in the limiting case α(x)p(x) ≡ n
We show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝ n in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small …