TY - JOUR
T1 - Semi-almost periodic Fourier multipliers on rearrangement-invariant spaces with suitable Muckenhoupt weights
AU - Fernandes, Cláudio António
AU - Karlovich, A. Yu
N1 - UID/MAT/00297/2019
PY - 2020/11/1
Y1 - 2020/11/1
N2 - Let X(R) be a separable rearrangement-invariant space and w be a suitable Muckenhoupt weight. We show that for any semi-almost periodic Fourier multiplier a on X(R, w) = { f: fw∈ X(R) } there exist uniquely determined almost periodic Fourier multipliers al, ar on X(R, w) , such that a=(1-u)al+uar+a0,for some monotonically increasing function u with u(- ∞) = 0 , u(+ ∞) = 1 and some continuous and vanishing at infinity Fourier multiplier a on X(R, w). This result extends previous results by Sarason (Duke Math J 44:357–364, 1977) for L2(R) and by Karlovich and Loreto Hernández (Integral Equ Oper Theor 62:85–128, 2008) for weighted Lebesgue spaces Lp(R, w) with weights in a suitable subclass of the Muckenhoupt class Ap(R).
AB - Let X(R) be a separable rearrangement-invariant space and w be a suitable Muckenhoupt weight. We show that for any semi-almost periodic Fourier multiplier a on X(R, w) = { f: fw∈ X(R) } there exist uniquely determined almost periodic Fourier multipliers al, ar on X(R, w) , such that a=(1-u)al+uar+a0,for some monotonically increasing function u with u(- ∞) = 0 , u(+ ∞) = 1 and some continuous and vanishing at infinity Fourier multiplier a on X(R, w). This result extends previous results by Sarason (Duke Math J 44:357–364, 1977) for L2(R) and by Karlovich and Loreto Hernández (Integral Equ Oper Theor 62:85–128, 2008) for weighted Lebesgue spaces Lp(R, w) with weights in a suitable subclass of the Muckenhoupt class Ap(R).
KW - Almost periodic function
KW - Boyd indices
KW - Fourier multiplier
KW - Muckenhoupt weight
KW - Rearrangement-invariant Banach function space
KW - Semi-almost periodic function
UR - http://www.scopus.com/inward/record.url?scp=85078802545&partnerID=8YFLogxK
U2 - 10.1007/s40590-020-00276-1
DO - 10.1007/s40590-020-00276-1
M3 - Article
AN - SCOPUS:85078802545
SN - 1405-213X
VL - 26
SP - 1135
EP - 1162
JO - Boletin de la Sociedad Matematica Mexicana
JF - Boletin de la Sociedad Matematica Mexicana
IS - 3
ER -