Multiplier transformations on $H^{p}$ spaces
Volume 131 / 1998
Studia Mathematica 131 (1998), 189-204
DOI: 10.4064/sm-131-2-189-204
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 $ℝ^n$.
