@article{article_958029, title={ON FUNCTION SPACES CHARACTERIZED BY THE WIGNER TRANSFORM}, journal={Journal of Universal Mathematics}, volume={4}, pages={188–200}, year={2021}, DOI={10.33773/jum.958029}, author={Kulak, Öznur}, keywords={Wigner transform, Essential Banach module, Approximate identity}, abstract={Let $\omega _{i}$ be weight
functions on $%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$, (i=1,2,3,4). In this work, we define $CW_{\omega _{1},\omega _{2},\omega _{3},\omega
_{4 }^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $ to be vector space of $\left( f,g\right) \in \left( L_{\omega
_{1 }^{p}\times L_{\omega _{2 }^{q}\right) \left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $ such that the $\tau -$Wigner transforms $W_{\tau }\left(
f,.\right) $ and $W_{\tau }\left( .,g\right) $ belong to $L_{\omega
_{3 }^{r}\left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
^{2}\right) $ and $L_{\omega _{4 }^{s}\left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
^{2}\right) $ respectively for $1\leq p,q,r,s<\infty $, $\tau \in \left(
0,1\right) $. We endow this space with a sum norm and prove that $%
CW_{\omega _{1},\omega _{2},\omega _{3},\omega _{4 }^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $ is a Banach space. We also show that $CW_{\omega _{1},\omega
_{2},\omega _{3},\omega _{4 }^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $ becomes an essential Banach module over $\left( L_{\omega
_{1 }^{1}\times L_{\omega _{2 }^{1}\right) \left( %TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $. We then consider approximate identities.}, number={2}, publisher={Gökhan ÇUVALCIOĞLU}, organization={Giresun University}