$H^p$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes

Jacek Dziubański, and Jacek Zienkiewicz. "$H^{p}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes." Colloquium Mathematicae 98.1 (2003): 5-38. <http://eudml.org/doc/284618>.

@article{JacekDziubański2003,
abstract = {Let A = -Δ + V be a Schrödinger operator on $ℝ^\{d\}$, d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of $H^\{p\}_\{A\}$ if the maximal function $sup_\{t>0\} |T_\{t\}f(x)|$ belongs to $L^\{p\}(ℝ^\{d\})$, where $\{T_\{t\}\}_\{t>0\}$ is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space $H^\{p\}_\{A\}$ admits a special atomic decomposition.},
author = {Jacek Dziubański, Jacek Zienkiewicz},
journal = {Colloquium Mathematicae},
keywords = {Schrödinger operator; reverse Hölder classes; -spaces},
language = {eng},
number = {1},
pages = {5-38},
title = {$H^\{p\}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes},
url = {http://eudml.org/doc/284618},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Jacek Dziubański
AU - Jacek Zienkiewicz
TI - $H^{p}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 1
SP - 5
EP - 38
AB - Let A = -Δ + V be a Schrödinger operator on $ℝ^{d}$, d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of $H^{p}_{A}$ if the maximal function $sup_{t>0} |T_{t}f(x)|$ belongs to $L^{p}(ℝ^{d})$, where ${T_{t}}_{t>0}$ is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space $H^{p}_{A}$ admits a special atomic decomposition.
LA - eng
KW - Schrödinger operator; reverse Hölder classes; -spaces
UR - http://eudml.org/doc/284618
ER -