A remark on extrapolation of rearrangement operators on dyadic $H^s$, 0 < s ≤ 1

Stefan Geiss, Paul F. X. Müller, and Veronika Pillwein. "A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1." Studia Mathematica 171.2 (2005): 196-205. <http://eudml.org/doc/286642>.

@article{StefanGeiss2005,
abstract = {For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_\{s\}$, 0 < s < 2, to be the linear extension of the map $(h_\{I\})/(|I|^\{1/s\}) ↦ (h_\{τ(I)\})(|τ(I)|^\{1/s\})$, where $h_\{I\}$ denotes the $L^\{∞\}$-normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_\{s₀\}$ is bounded on $H^\{s₀\}$, then for all 0 < s < 2 the operator $T_\{s\}$ is bounded on $H^\{s\}$.},
author = {Stefan Geiss, Paul F. X. Müller, Veronika Pillwein},
journal = {Studia Mathematica},
keywords = {rearrangement operator; dyadic Hardy space; extrapolation},
language = {eng},
number = {2},
pages = {196-205},
title = {A remark on extrapolation of rearrangement operators on dyadic $H^\{s\}$, 0 < s ≤ 1},
url = {http://eudml.org/doc/286642},
volume = {171},
year = {2005},
}

TY - JOUR
AU - Stefan Geiss
AU - Paul F. X. Müller
AU - Veronika Pillwein
TI - A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 2
SP - 196
EP - 205
AB - For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$, 0 < s < 2, to be the linear extension of the map $(h_{I})/(|I|^{1/s}) ↦ (h_{τ(I)})(|τ(I)|^{1/s})$, where $h_{I}$ denotes the $L^{∞}$-normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s₀}$ is bounded on $H^{s₀}$, then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$.
LA - eng
KW - rearrangement operator; dyadic Hardy space; extrapolation
UR - http://eudml.org/doc/286642
ER -