Počet záznamů: 1

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

  1. 1.
    0334985 - MU-W 2010 RIV ES eng J - Článek v odborném periodiku
    Announi, M. - Grafakos, L. - Honzík, Petr
    On an inequality of Sagher and Zhou concerning Stein's lemma.
    [O nerovnosti Saghrera a Zhoua vztahující se k Steinovu lemmatu.]
    Collectanea Mathematica. Roč. 60, č. 3 (2009), s. 297-306 ISSN 0010-0757
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: lacunary series * sequences * Rademacher functions
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.389, rok: 2009

    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.

    Ukazeme dva nové způsoby, jak dokázat nerovnost Saghera a Zhoua.
    Trvalý link: http://hdl.handle.net/11104/0179583
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