On the L∞$$ {L}∧{\infty } $$-regularity for fractional Orlicz problems via Moser's iteration

Lp$$ {L}<^>p $$ estimates for the fractional phi$$ \Phi $$-Laplacian operator defined in bounded domains are established, where the nonlinearity is subcritical or critical in a suitable sense. Furthermore, using some fine estimates together with Moser's iteration, we prove that any weak solution for fractional phi$$ \Phi $$-Laplacian operator defined in bounded domains belongs to L infinity(omega)$$ {L}<^>{\infty}\left(\Omega \right) $$, under appropriate hypotheses on the N$$ N $$-function phi$$ \Phi $$. Using the Orlicz space and taking into account the fractional setting for our problem, the main results are stated for a huge class of nonlinear operators and nonlinearities.