The Hausdorff operators on the real Hardy spaces $H^p\left(ℝ\right)$

Yuichi Kanjin. "The Hausdorff operators on the real Hardy spaces $H^{p}(ℝ)$." Studia Mathematica 148.1 (2001): 37-45. <http://eudml.org/doc/285356>.

@article{YuichiKanjin2001,
abstract = {We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space $H^\{p\}(ℝ)$, 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on $H^\{p\}(ℝ)$, 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^\{p\}(ℝ)$.},
author = {Yuichi Kanjin},
journal = {Studia Mathematica},
keywords = {Hausdorff operator; Cesàro operator; real Hardy space; Fourier transform; atomic decomposition; molecular characterization},
language = {eng},
number = {1},
pages = {37-45},
title = {The Hausdorff operators on the real Hardy spaces $H^\{p\}(ℝ)$},
url = {http://eudml.org/doc/285356},
volume = {148},
year = {2001},
}

TY - JOUR
AU - Yuichi Kanjin
TI - The Hausdorff operators on the real Hardy spaces $H^{p}(ℝ)$
JO - Studia Mathematica
PY - 2001
VL - 148
IS - 1
SP - 37
EP - 45
AB - We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space $H^{p}(ℝ)$, 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on $H^{p}(ℝ)$, 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^{p}(ℝ)$.
LA - eng
KW - Hausdorff operator; Cesàro operator; real Hardy space; Fourier transform; atomic decomposition; molecular characterization
UR - http://eudml.org/doc/285356
ER -