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Polynomial estimates on real and complex $L_p(\mu )$ spaces

Tom 235 / 2016

Marios K. Papadiamantis, Yannis Sarantopoulos Studia Mathematica 235 (2016), 31-45 MSC: Primary 46G25; Secondary 47H60, 46E15. DOI: 10.4064/sm8484-7-2016 Opublikowany online: 4 October 2016

Streszczenie

In his commentary to Problem 73 of Mazur and Orlicz in the Scottish Book, L. A. Harris raised the following natural generalization: Let $X$ be a Banach space, let $k_1,\ldots,k_n$ be nonnegative integers whose sum is $m$ and let $c(k_1, \ldots, k_n; X)$ be the smallest number with the property that if $L$ is any symmetric $m$-linear mapping of one real normed linear space into another, then $|L(x_1^{k_1}\ldots x_n^{k_n})|\leq c(k_1,\ldots,k_n; X)\|\widehat L\|$, where $\widehat L$ is the $m$-homogeneous polynomial associated to $L$. In this paper, we give estimates in the case of a real $L_p(\mu)$ space using three different techniques and we get optimal results in some special cases.

Autorzy

  • Marios K. PapadiamantisDepartment of Mathematics
    National Technical University
    Zografou Campus 157 80, Athens, Greece
    e-mail
  • Yannis SarantopoulosDepartment of Mathematics
    National Technical University
    Zografou Campus 157 80, Athens, Greece
    e-mail

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