On highly nonintegrable functions and homogeneous polynomials

ArticleOriginal scientific text

Title

Authors ¹

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 . 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.

homogeneous polynomials, highly nonintegrable holomorphic function

A. B. Aleksandrov, Proper holomorphic maps from the ball into a polydisc, Dokl. Akad. Nauk SSSR 286 (1986), 11-15 (in Russian).
P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math., to appear.
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.
W. Rudin, Function Theory in the Unit Ball of $ℂ^{n}$ , Springer, New York, 1980.
J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), 107-116.
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).
P. Wojtaszczyk, On values of homogeneous polynomials in discrete sets of points, Studia Math. 84 (1986), 97-104.