On highly nonintegrable functions and homogeneous polynomials

P. Wojtaszczyk

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 3, page 245-251
  • ISSN: 0066-2216

Abstract

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

How to cite

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P. Wojtaszczyk. "On highly nonintegrable functions and homogeneous polynomials." Annales Polonici Mathematici 65.3 (1997): 245-251. <http://eudml.org/doc/269970>.

@article{P1997,
abstract = {We construct a sequence of homogeneous polynomials on the unit ball $_d$ in $ℂ^d$ which are big at each point of the unit sphere . As an application we construct a holomorphic function on $_d$ which is not integrable with any power on the intersection of $_d$ with any complex subspace.},
author = {P. Wojtaszczyk},
journal = {Annales Polonici Mathematici},
keywords = {homogeneous polynomials; highly nonintegrable holomorphic function; highly nonintegrable functions},
language = {eng},
number = {3},
pages = {245-251},
title = {On highly nonintegrable functions and homogeneous polynomials},
url = {http://eudml.org/doc/269970},
volume = {65},
year = {1997},
}

TY - JOUR
AU - P. Wojtaszczyk
TI - On highly nonintegrable functions and homogeneous polynomials
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 3
SP - 245
EP - 251
AB - We construct a sequence of homogeneous polynomials on the unit ball $_d$ in $ℂ^d$ which are big at each point of the unit sphere . As an application we construct a holomorphic function on $_d$ which is not integrable with any power on the intersection of $_d$ with any complex subspace.
LA - eng
KW - homogeneous polynomials; highly nonintegrable holomorphic function; highly nonintegrable functions
UR - http://eudml.org/doc/269970
ER -

References

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  1. [1] A. B. Aleksandrov, Proper holomorphic maps from the ball into a polydisc, Dokl. Akad. Nauk SSSR 286 (1986), 11-15 (in Russian). 
  2. [2] P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math., to appear. Zbl0887.32004
  3. [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. Zbl0442.30032
  4. [4] W. Rudin, Function Theory in the Unit Ball of ℂ n , Springer, New York, 1980. 
  5. [5] J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), 107-116. Zbl0522.32004
  6. [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. [7] P. Wojtaszczyk, On values of homogeneous polynomials in discrete sets of points, Studia Math. 84 (1986), 97-104. Zbl0611.32006

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