We consider the first boundary-value problem for a second-order degenerate elliptic-parabolic equation with, generally speaking, discontinuous coefficients. The matrix of leading coefficients satisfies the parabolic Cordes condition with respect to space variables. We prove that the generalized solution of the problem belongs to the Hölder space C 1+λ if the right-hand side f belongs to L p , p n > .
Let L = −∆ H n + V be a Schrödinger operator on the Heisenberg groups H n , where the non-negative potential V belongs to the reverse Hölder class RH Q/2 and Q is the homogeneous dimension of H n . Let b belong to a new BMO θ (H n , ρ) space, and let I L β be the fractional integral operator associated with L. In this paper, we study the boundedness of the operator I
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