Multiplier transformations on $H^p$ spaces

Chen, Daning, and Fan, Dashan. "Multiplier transformations on $H^{p}$ spaces." Studia Mathematica 131.2 (1998): 189-204. <http://eudml.org/doc/216575>.

@article{Chen1998,
abstract = {The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator $(Tf)^(x) = λ(x)f̂(x)$$(λ ∈ C(ℝ^n))$ is bounded on $H^p(ℝ^n)$ if and only if the restriction $\{λ(εm)\}_\{m∈Λ\}$ is an $H^p(T^n)$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^n$.},
author = {Chen, Daning, Fan, Dashan},
journal = {Studia Mathematica},
keywords = {multiplier operator; bounded operator},
language = {eng},
number = {2},
pages = {189-204},
title = {Multiplier transformations on $H^\{p\}$ spaces},
url = {http://eudml.org/doc/216575},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Chen, Daning
AU - Fan, Dashan
TI - Multiplier transformations on $H^{p}$ spaces
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 2
SP - 189
EP - 204
AB - The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator $(Tf)^(x) = λ(x)f̂(x)$$(λ ∈ C(ℝ^n))$ is bounded on $H^p(ℝ^n)$ if and only if the restriction ${λ(εm)}_{m∈Λ}$ is an $H^p(T^n)$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^n$.
LA - eng
KW - multiplier operator; bounded operator
UR - http://eudml.org/doc/216575
ER -