منابع مشابه
Differentiation in lacunary directions.
Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].
متن کاملDifferentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
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We show that the maximal operator below, defined initially for Schwartz functions f on the plane, extends to a bounded operator from Lp(R2) into itself for 1 < p < ∞. sup k∈Z ∣∣p.v. ∫ f(x− (1, 2)y) dy y ∣∣. The maximal function variant was established by Nagel, Stein and Wainger in 1978 [7]. 1 The Maximal Theorem For a smooth rapidly decreasing function f on the plane and a nonzero vector v ∈ R...
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متن کاملLacunary Statistical Convergence and Inclusion Properties between Lacunary Methods
A lacunary sequence is an increasing integer sequence θ = {kr } such that kr − kr−1 → ∞ as r → ∞. A sequence x is called sθ-convergent to L provided that for each ε > 0, limr (1/(kr −kr−1)){the number of kr−1 < k ≤ kr : |xk−L| ≥ ε} = 0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1978
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.75.3.1060