On an inequality of Sagher and Zhou concerning Stein's lemma

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On an inequality of Sagher and Zhou concerning Stein's lemma

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Collectanea Mathematica

ISSN

0010-0757

e-ISSN

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Volume of the periodical

60

Issue of the periodical within the volume

3

Country of publishing house

ES - SPAIN

Number of pages

10

Pages from-to

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UT code for WoS article

000270375800005

EID of the result in the Scopus database

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