The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey representations of continuous linear maps for harmonic functions in the set of all closed bounded conve...

If u ∈ H(M,N) is a weakly J-holomorphic map from a compact without boundary almost hermitian manifold (M, j, g) into another compact without boundary almost hermitian manifold (N, J, h). Then it is smooth near any point x where Du has vanishing Morrey norm M2,2m−2, with 2m =dim(M). Hence H2m−2measure of the singular set for a stationary J-holomorphic map is zero. Blow-up analysis and the energy...

We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift −ut + Lu = −ut + ∑ ij aijDiju + ∑ biDiu = 0 (≥ 0, ≤ 0) in some domain Ω ⊂ Rn+1. We prove a variant of Aleksandrov-BakelmanPucci-Krylov-Tso estimate with Lp norm of the inhomogeneous term for some number p < n+1. Based on it, we derive the growth theorems and the interior Harnack ineq...

In this paper, we establish the boundedness of p -adic Riesz potential on Morrey-Herz spaces, as well id="M3"> λ -central BMO estimates for multilinear commutators id="M4"> spaces.