TY - JOUR
T1 - Two-sided weighted Fourier inequalities
AU - Liflyand, E.
AU - Tikhonov, Sergey
PY - 2012
Y1 - 2012
N2 - Fourier transform estimates for ! !f !Lq,w" via ! f !L p,w from above and
from below are studied. For p = q, equivalence results, i.e.,
C1! f !L p,w ≤ ! !f !L p,w" ≤ C2! f !L p,w , w"(x) = w(1/x)x p−2, 1 ≤ p < ∞,
are shown to be valid for functions from certain classes under the Muckenhoupt
conditions: w ∈ Ap or w ∈ A2p. Sharpness of these conditions is prov
AB - Fourier transform estimates for ! !f !Lq,w" via ! f !L p,w from above and
from below are studied. For p = q, equivalence results, i.e.,
C1! f !L p,w ≤ ! !f !L p,w" ≤ C2! f !L p,w , w"(x) = w(1/x)x p−2, 1 ≤ p < ∞,
are shown to be valid for functions from certain classes under the Muckenhoupt
conditions: w ∈ Ap or w ∈ A2p. Sharpness of these conditions is prov
UR - https://www.researchgate.net/publication/267018399_Two-sided_weighted_Fourier_inequalities
M3 - Article
VL - 11
SP - 341
EP - 362
JO - ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA, CLASSE DI SCIENZE
JF - ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA, CLASSE DI SCIENZE
IS - 5
ER -