We obtain sharp ranges of-boundedness for domains in a wide class of Reinhardt domains
representable as sublevel sets of monomials, by expressing them as quotients of simpler …

Weighted Sobolev estimates of∂ on domains covered by polydiscs Page 1 Weighted Sobolev
estimates of∂ on domains covered by polydiscs Yuan Yuan and Yuan Zhang Abstract This …

We study the $ L^ p $ regularity of the Bergman projection $ P $ over the symmetrized
polydisc in $\mathbb C^ n $. We give a decomposition of the Bergman projection on the …

In this paper, we study the weak-type regularity of the Bergman projection on monomial
polyhedra, which is a wide class of bounded singular pseudoconvex Reinhardt domains …

The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt
domain by a finite subgroup of $ U (n) $. The Szeg\H {o} projection on the quotient domain …

We begin this thesis by a brief introduction to the $\bar {\partial} $-problem in several
complex variables and the classical $ L^ 2$ Theorem of $\bar {\partial} $. We then introduce …