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On weighted Bergman kernels of bounded domains

Sorin Dragomir (1994)

Studia Mathematica

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains Ω N for admissible weights a L ¹ ( Ω ) .

Pointwise estimates for the weighted Bergman projection kernel in n , using a weighted L 2 estimate for the ¯ equation

Henrik Delin (1998)

Annales de l'institut Fourier

Weighted L 2  estimates are obtained for the canonical solution to the equation in L 2 ( n , e - φ d λ ) , where Ω is a pseudoconvex domain, and φ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in L 2 ( n , e - φ d λ ) . The weight is used to obtain a factor e - ϵ ρ ( z , ζ ) in the estimate of the kernel, where ρ is the distance function in the Kähler metric given by the metric form i φ .

Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels

E. H. Youssfi (2002)

Studia Mathematica

We consider a large class of convex circular domains in M m , n ( ) × . . . × M m d , n d ( ) which contains the oval domains and minimal balls. We compute their Bergman and Szegő kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.

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