On highly nonintegrable functions and homogeneous polynomials

• Autorzy: P. Wojtaszczyk
• Języki publikacji: EN

Abstrakty

EN

We construct a sequence of homogeneous polynomials on the unit ball $𝔹_d$ in $ℂ^d$ which are big at each point of the unit sphere 𝕊. As an application we construct a holomorphic function on $𝔹_d$ which is not integrable with any power on the intersection of $𝔹_d$ with any complex subspace.

Słowa kluczowe

EN

homogeneous polynomials; highly nonintegrable holomorphic function

Kategorie tematyczne

• 32A05: Power series, series of functions
• 32A35: H p -spaces, Nevanlinna spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 3
• Strony: 245-251

Daty

wydano

1997

otrzymano

1996-05-06

Twórcy

autor

P. Wojtaszczyk

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] A. B. Aleksandrov, Proper holomorphic maps from the ball into a polydisc, Dokl. Akad. Nauk SSSR 286 (1986), 11-15 (in Russian).
• [2] P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math., to appear.
• [3] A. Nakamura, F. Ohya and H. Watanabe, On some properties of functions in weighted Bergman spaces, Proc. Fac. Sci. Tokyo Univ. 15 (1979), 33-44.
• [4] W. Rudin, Function Theory in the Unit Ball of $ℂ^n$, Springer, New York, 1980.
• [5] J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), 107-116.
• [6] S. V. Shvedenko, On the Taylor coefficients of functions from Bergman spaces in the polydisk, Dokl. Akad. Nauk SSSR 283 (1985), 325-328 (in Russian).
• [7] P. Wojtaszczyk, On values of homogeneous polynomials in discrete sets of points, Studia Math. 84 (1986), 97-104.