TY  - JOUR
T1  - ON FUNCTION SPACES CHARACTERIZED BY THE WIGNER TRANSFORM
AU  - Kulak, Öznur
PY  - 2021
DA  - July
Y2  - 2021
DO  - 10.33773/jum.958029
JF  - Journal of Universal Mathematics
JO  - JUM
PB  - Gökhan ÇUVALCIOĞLU
WT  - DergiPark
SN  - 2618-5660
SP  - 188
EP  - 200
VL  - 4
IS  - 2
LA  - en
AB  - Let $\omega _{i}$  be weightfunctions 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.
KW  - Wigner transform
KW  - Essential Banach module
KW  - Approximate identity
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UR  - https://doi.org/10.33773/jum.958029
L1  - https://dergipark.org.tr/tr/download/article-file/1845077
ER  -