Inequalities for Walsh like random variables

D. Hajela

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-4

Abstract:

Let ( X n ) n ≥ 1 be a sequence of mean zero independent random variables. Let W k = { ∏ j = 1 k X i j | 1 ≤ i 1 < i 2 … < i k } , Y k = ⋃ j ≤ k W j and let [ Y k ] be the linear span of Y k . Assume δ ≤ | X n | ≤ K for some δ > 0 and K > 0 and let C ( p , m ) = 16 ( 5 2 p 2 p − 1 ) m − 1 p log p ( K δ ) m for 1 < p < ∞ . We show that for f ∈ [ Y m ] the following inequalities hold: ‖ f ‖ 2 ≤ ‖ f ‖ p ≤ C ( p , m ) ‖ f ‖ 2 for 2 < p < ∞ ‖ f ‖ 2 ≤ C ( q , m ) ‖ f ‖ p ≤ C ( q , m ) ‖ f ‖ 2 for 1 < p < 2 , 1 p + 1 q = 1 and ‖ f ‖ 2 ≤ C ( 4 , m ) 2 ‖ f ‖ 1 ≤ C ( 4 , m ) 2 ‖ f ‖ 2 . These generalize various well known inequalities on Walsh functions.

Date: 1990
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/13/346835.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/13/346835.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:346835

DOI: 10.1155/S0161171290000527

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().