Higher Hölder regularity for fractional $(p,q)$-Laplace equations

We study the fractional $(p,q)$-Laplace equation $$(-{\mathrm{\Delta }}_p{)}^{s}u+(-{\mathrm{\Delta }}_q{)}^{t}u=0$$ for $s,t\in (0,1)$ and $p,q\in (1,\mathrm{\infty })$. We establish Hölder estimates with an explicit exponent. As a consequence, we derive a Liouville-type theorem. Our approach builds on techniques previously developed for the fractional $p$-Laplace equation, relying on a Moser-type iteration for difference quotients.