Number of the records: 1
On an inequality of Sagher and Zhou concerning Stein's lemma
- 1.
SYSNO ASEP 0334985 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On an inequality of Sagher and Zhou concerning Stein's lemma Title O nerovnosti Saghrera a Zhoua vztahující se k Steinovu lemmatu Author(s) Announi, M. (US)
Grafakos, L. (US)
Honzík, Petr (MU-W) RID, SAISource Title Collectanea Mathematica. - : Springer - ISSN 0010-0757
Roč. 60, č. 3 (2009), s. 297-306Number of pages 10 s. Language eng - English Country ES - Spain Keywords lacunary series ; sequences ; Rademacher functions Subject RIV BA - General Mathematics CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000270375800005 Annotation We provide two alternative proofs of the following formulation of Stein's lemma obtained by Sagher and Zhou [6]: there exists a constant A > 0 such that for any measurable set E subset of [0, 1], vertical bar E vertical bar not equal 0, there is an integer N that depends only on E such that for any square-summable real-valued sequence {c(k)}(k=0)(infinity) we have: A.Sigma(k > N)vertical bar c(k)vertical bar(2) <= sup(I) inf(a is an element of R) 1/vertical bar I vertical bar integral(I boolean AND E) vertical bar f(t) - a vertical bar(2) dt, (1)where the supremum is taken over all dyadic intervals I and f(t) = Sigma(infinity)(k=0)c(k)(sic)(k)(t), where (sic)(k) denotes the kth Rademacher function. The first proof does not rely on Khintchine's inequality while the second is succinct and applies to general lacunary Walsh series. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
Number of the records: 1