Weak-type regularity for the Bergman projection over N-dimensional classical Hartogs triangles

Abstract

Abstract In this paper, we study the weak-type regularity of the Bergman projection on n-dimensional classical Hartogs triangles. We extend the results of Huo–Wick on the 2-dimensional classical Hartogs triangle to the n-dimensional classical Hartogs triangle and show that the Bergman projection is of weak type at the upper endpoint of L q $L^{q}$ -boundedness but not of weak type at the lower endpoint of L q $L^{q}$ -boundedness.

Keywords

• Weak-type
• Bergman projection
• n-dimensional classical Hartogs triangle
• Bergman kernel