# On highly nonintegrable functions and homogeneous polynomials

Annales Polonici Mathematici (1997)

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

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topP. 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

top- [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. Zbl0887.32004
- [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] W. Rudin, Function Theory in the Unit Ball of ${\u2102}^{n}$, 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. Zbl0522.32004
- [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. Zbl0611.32006

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