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We study a class of nonlocal double phase problems with discontinuouscoefficients. A local self-improving property and a higher H\"older continuityresult for weak solutions to such problems are obtained under the assumptionsthat the associated coefficient functions are of type VMO (vanishing meanoscillation) and that the principal coefficient depends not only on thevariables but also on the solution itself.

Regularity results for a class of nonlocal double phase equations with VMO coefficients