Abstract
In this paper, we study the global boundary regularity of the - equation on an annulus domain between two strictly -convex domains with smooth boundaries in for some bidegree. To this finish, we first show that the -operator has closed range on and the -Neumann operator exists and is compact on for all , . We also prove that the -Neumann operator and the Bergman projection operator are continuous on the Sobolev space , , , and . Consequently, the -existence theorem for the -equation on such domain is established. As an application, we obtain a global solution for the equation with Holder and -estimates on strictly -concave domain with smooth boundary in , by using the local solutions and applying the pushing out method of Kerzman (Commun Pure Appl Math 24:301-380, 1971).