Certain schur-hadamard multipliers m the spaces cp

Jonathan Arazy

doi:10.1090/S0002-9939-1982-0663866-5

Certain schur-hadamard multipliers m the spaces c_p

Jonathan Arazy

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let/be a continuously differentiable function on [—1, 1] satisfying |f’(t)| < C\t\^α for some 0 < C, α < ∞ and all — 1 ≤ t ≤ 1, and let λ = (λ_i) Є l_r satisfy — 1 ≤ λ_i ≤ 1 for all i. Then αf, λ=(f(λ_i) - f(λ_j) /λ_i- λ_j) is a Schur-Hadamard multiplier from C_p i into C_P2 for all pi, p2 satisfying 1 ≤ p₂ ≤ 2 ≤ p₁ ≤ ∞ and p₂^-1 ≤ p₁^-1 + α/r.

Original language	English
Pages (from-to)	59-64
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	86
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1982-0663866-5
State	Published - Sep 1982

Keywords

Cp spaces
Schur-Hadamard multipliers
Triangular projection

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9939-1982-0663866-5

Cite this

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title = "Certain schur-hadamard multipliers m the spaces cp",

abstract = "Let/be a continuously differentiable function on [—1, 1] satisfying |f{\textquoteright}(t)| < C\textbackslash{}t\textbackslash{}α for some 0 < C, α < ∞ and all — 1 ≤ t ≤ 1, and let λ = (λi) Є lr satisfy — 1 ≤ λi ≤ 1 for all i. Then αf, λ=(f(λi) - f(λj) /λi- λj) is a Schur-Hadamard multiplier from Cp i into CP2 for all pi, p2 satisfying 1 ≤ p2 ≤ 2 ≤ p1 ≤ ∞ and p2-1 ≤ p1-1 + α/r.",

keywords = "Cp spaces, Schur-Hadamard multipliers, Triangular projection",

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N2 - Let/be a continuously differentiable function on [—1, 1] satisfying |f’(t)| < C\t\α for some 0 < C, α < ∞ and all — 1 ≤ t ≤ 1, and let λ = (λi) Є lr satisfy — 1 ≤ λi ≤ 1 for all i. Then αf, λ=(f(λi) - f(λj) /λi- λj) is a Schur-Hadamard multiplier from Cp i into CP2 for all pi, p2 satisfying 1 ≤ p2 ≤ 2 ≤ p1 ≤ ∞ and p2-1 ≤ p1-1 + α/r.

AB - Let/be a continuously differentiable function on [—1, 1] satisfying |f’(t)| < C\t\α for some 0 < C, α < ∞ and all — 1 ≤ t ≤ 1, and let λ = (λi) Є lr satisfy — 1 ≤ λi ≤ 1 for all i. Then αf, λ=(f(λi) - f(λj) /λi- λj) is a Schur-Hadamard multiplier from Cp i into CP2 for all pi, p2 satisfying 1 ≤ p2 ≤ 2 ≤ p1 ≤ ∞ and p2-1 ≤ p1-1 + α/r.

KW - Cp spaces

KW - Schur-Hadamard multipliers

KW - Triangular projection

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