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Fractional series operators on discrete Hardy spaces

Rocha, P.

Acta mathematica Hungarica, 2022-10, Vol.168 (1), p.202-216 [Periódico revisado por pares]

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Título:
Fractional series operators on discrete Hardy spaces
Autor: Rocha, P.
Assuntos: Mathematics ; Mathematics and Statistics ; Operators (mathematics)
É parte de: Acta mathematica Hungarica, 2022-10, Vol.168 (1), p.202-216
Descrição: For 0 ≤ γ < 1 and a sequence b = { b ( i ) } i ∈ Z we consider the fractional operator T α , β defined formally by ( T α , β b ) ( j ) = ∑ i ≠ ± j b ( i ) | i - j | α | i + j | β ( j ∈ Z ) , where α , β > 0 and α + β = 1 - γ . The main aim of this note is to prove that the operator T α , β is bounded from H p ( Z ) into ℓ q ( Z ) for 0 < p < 1 γ and 1 q = 1 p - γ . For α = β = 1 - γ 2 we show that there exists ϵ ∈ ( 0 , 1 3 ) such that for every 0 ≤ γ < ϵ the operator T 1 - γ 2 , 1 - γ 2 is not bounded from H p ( Z ) into H q ( Z ) for 0 < p ≤ 1 1 + γ and 1 q = 1 p - γ .
Editor: Cham: Springer International Publishing
Idioma: Inglês

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