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서지반출
PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS
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  • PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS
  • PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS
저자명
Revesz. Szilard-Gy.,Sarantopoulos. Yannis
간행물명
Journal of the Korean Mathematical Society
권/호정보
2004년|41권 1호|pp.157-174 (18 pages)
발행정보
대한수학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
서지반출

기타언어초록

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(mu)$ spaces. In the case $1;{leq};p;{leq};2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.