The Cauchy-Riemann Complex

Koppelman formulas on the A1-singularity

“…On smooth varieties, these extensions coincide by Friedrichs' extension lemma, see for example [LM,Theorem V.2.6]. From our results below, it will follow that in L 2 on the A 1 -singularity, the∂ w and∂ s operators do indeed coincide.…”

Lp ‐estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains

“…, and so the well-known mapping property of P in that case as established by Phongard Stein (see [8] …”

“…The methods from [8] or [1] can be easily applied even in the case of kernels with mixed singularities (which appear in the kernels of T 0 ). We include a proof here ourselves dealing with the admissible kernels of type (3.1) defined above for the sake of completeness.…”

“…Let > 0 and define D − = {r < − }. In order to establish Lemma 2.1 in our case, we exhaust D by the domains D − and introduce operators P 0 and T 0 as defined in [8] for smooth domains, the operators given as volume integrals. Now, for f ∈ C 1 (D) and z ∈ D, we have…”

“…Function theory on smooth strictly pseudoconvex domains is by now well understood, due to the work of many authors, see [8] for results and historical comments. Non-smooth domains, i.e.…”