Double phase meets Muckenhoupt

In this paper we generalize the famous result of [FKS] to the double phase model. In particular, we work with minimal assumptions on the modulating coefficient by introducing a Muckenhoupt-type condition on generalized Orlicz spaces. We develop a complete theory equivalent to that of classical Muckenhoupt weights, including the boundedness of the maximal operator and Sobolev-Poincare estimates. We combine this with the De~Giorgi technique to show Hölder continuity of the solutions.

💡 Research Summary

The paper “Double Phase Meets Muckenhoupt” develops a regularity theory for the double‑phase functional
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