Estimates for invariant metrics on $\mathbb C$-convex domains

Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

Estimates of Invariant Metrics on Pseudoconvex Domains near Boundaries with Constant Levi Ranks

Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given. Mathematics Subject Classification (2000): 32F45; 32T27.

Estimates for Weighted Bergman Projections on Pseudo-convex Domains of Finite Type in C

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in C. The main result is obtained for weights equal to a non-negative rational power of the absolute value of a special defining function ρ of the domain: we prove (weighted) Sobolev-L and Lipschitz estimates for domains in C2 (or, more generally, for ...

Sobolev and Hh Older Estimates for @ on Bounded Convex Domains in C 2

On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

Abstract. Using Maz’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in R. For n ≥ 8, combined with a result in [S2], these estimates lead to the solvability of the L Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of p. In the case of convex domains, the estimates allow u...