BOHR'S INEQUALITIES IN n-INNER PRODUCT SPACES

  • Cheung, W.S. (DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF HONG KONG) ;
  • Cho, Y.S. (DEPARTMENT OF MATHEMATICS EDUCATION AND THE RINS, GYEONGSANG NATIONAL UNIVERSITY) ;
  • Pecaric, J. (FACULTY OF TEXTILE TECHNOLOGY, UNIVERSITY OF ZAGREB) ;
  • Zhao, D.D. (DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF HONG KONG)
  • Published : 2007.05.31

Abstract

The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.