## Estimates for the Bergman and Szegö kernels in $${\mathbb{C}}^ 2$$.(English)Zbl 0667.32016

Some results of this paper are announced in the previous paper of the same authors [Bull. Am. Math. Soc., New Ser. 18, No.1, 55-59 (1988; Zbl 0642.32014)]. They study Bergman-Szegö projection operators on pseudoconvex domain of finite type in $${\mathbb{C}}^ 2$$ and obtain results of the three kinds; (i) The size estimates. (ii) The cancellation properties expressed on suitable bump functions. (iii) The sharp mapping properties on function spaces.
The main key is the possibility of using scaling. They also perspect past and recent topics.
Reviewer: J.Kajiwara

### MSC:

 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 32T99 Pseudoconvex domains

Zbl 0642.32014
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