- Tytuł:
- An inverse Sidon type inequality
- Autorzy:
- Fridli, S.
- Powiązania:
- https://bibliotekanauki.pl/articles/1292682.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Sidon type inequalities
Hardy spaces
convergence classes - Opis:
- Sidon proved the inequality named after him in 1939. It is an upper estimate for the integral norm of a linear combination of trigonometric Dirichlet kernels expressed in terms of the coefficients. Since the estimate has many applications for instance in $L^1$ convergence problems and summation methods with respect to trigonometric series, newer and newer improvements of the original inequality has been proved by several authors. Most of them are invariant with respect to the rearrangement of the coefficients. Although the newest results are close to best possible, no nontrivial lower estimate has been given so far. The aim of this paper is to give the best rearrangement invariant function of coefficients that can be used in a Sidon type inequality. We also show that it is equivalent to an Orlicz type and a Hardy type norm. Examples of applications are also given.
- Źródło:
-
Studia Mathematica; 1993, 105, 3; 283-308
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł