Properties of the Sobolev space $H_k^{s,s^{\text{'}}}$

Henryk Kołakowski. "Properties of the Sobolev space $H_k^{s,s^{\prime }}$." Annales Polonici Mathematici 71.2 (1999): 199-209. <http://eudml.org/doc/262677>.

@article{HenrykKołakowski1999,
abstract = {Let n ≥ 2 and $H_k^\{s,s^\{\prime \}\} = \{u∈ S^\{\prime \}(ℝ^n): ∥u∥_\{s,s^\{\prime \}\} < ∞\}$, where $∥u∥²_\{s,s^\{\prime \}\} = (2π)^\{-n\} ∫(1+|ξ|²)^s (1+|ξ^\{\prime \}|²)^\{s^\{\prime \}\}|Fu(ξ)|²dξ $, $Fu(ξ) = ∫e^\{-ixξ\} u(x) dx$, $ξ^\{\prime \}∈ ℝ^k$, k < n. We prove that for some s,s’ the space $H^\{s,s^\{\prime \}\}_k$ is a multiplicative algebra.},
author = {Henryk Kołakowski},
journal = {Annales Polonici Mathematici},
keywords = {multiplicative algebra; Littlewood double decomposition; Fourier transform; microlocal regularity; nonlinear boundary value problems},
language = {eng},
number = {2},
pages = {199-209},
title = {Properties of the Sobolev space $H_k^\{s,s^\{\prime \}\}$},
url = {http://eudml.org/doc/262677},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Henryk Kołakowski
TI - Properties of the Sobolev space $H_k^{s,s^{\prime }}$
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 2
SP - 199
EP - 209
AB - Let n ≥ 2 and $H_k^{s,s^{\prime }} = {u∈ S^{\prime }(ℝ^n): ∥u∥_{s,s^{\prime }} < ∞}$, where $∥u∥²_{s,s^{\prime }} = (2π)^{-n} ∫(1+|ξ|²)^s (1+|ξ^{\prime }|²)^{s^{\prime }}|Fu(ξ)|²dξ $, $Fu(ξ) = ∫e^{-ixξ} u(x) dx$, $ξ^{\prime }∈ ℝ^k$, k < n. We prove that for some s,s’ the space $H^{s,s^{\prime }}_k$ is a multiplicative algebra.
LA - eng
KW - multiplicative algebra; Littlewood double decomposition; Fourier transform; microlocal regularity; nonlinear boundary value problems
UR - http://eudml.org/doc/262677
ER -