Processing math: 0%

Wykorzystujemy pliki cookies aby ułatwić Ci korzystanie ze strony oraz w celach analityczno-statystycznych.

JEDNOSTKA NAUKOWA KATEGORII A+

Polynomial estimates on real and complex 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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek