Inequalities for integral operators in Hölder–Morrey spaces on differential forms

The Hölder–Morrey spaces $\Lambda _{\kappa}^{p,\tau}(\Omega ,\wedge ^{l})$ Λ κ p , τ ( Ω , ∧ l ) are proposed in this paper. The imbedding inequalities for homotopy operator are derived in Hölder–Morrey spaces on differential forms. The Hölder continuity for Riesz potential with envelope function is deduced. As application, some composite theorems, which are associated with conjugate A-harmonic equations on differential forms, are given.