Displaying similar documents to “Removable sets for holomorphic functions of several complex variables.”

The Bergman kernel of the minimal ball and applications

Karl Oeljeklaus, Peter Pflug, El Hassan Youssfi (1997)

Annales de l'institut Fourier

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In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in ℂ n that extends the euclidean norm in ℝ n and give some applications.

A maximum principle for the Bergman space.

Boris Korenblum (1991)

Publicacions Matemàtiques

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Let f(z) and g(z) be holomorphic in the open unit disk D and let Zf and Zg be their zero sets. If Zf ⊃ Zg and |f(z)| ≥ |g(z)| (1/2 e-2 < |z| < 1), then || f || ≥ || g || where || · || is the Bergman norm: || f ||2 = π-1 ∫D |f(z)|2 dm (dm is the Lebesgue area measure).

Orthogonal polynomials and middle Hankel operators on Bergman spaces

Lizhong Peng, Richard Rochberg, Zhijian Wu (1992)

Studia Mathematica

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We introduce a sequence of Hankel style operators H k , k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the H k and show, among other things, that H k are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.

Hausdorff measures and the Morse-Sard theorem.

Carlos Gustavo T. de A. Moreira (2001)

Publicacions Matemàtiques

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Let F : U ⊂ R → R be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ C, if we set C(F) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + (n-p)/(k+α)) of F(C(F)) is zero.