COMPOSITION OPERATORS ON WIENER AMALGAM SPACES
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For a complex function $F$ on $\mathbb{C}$, we study the associated composition operator $T_{F}(f):=F\circ f=F(f)$ on Wiener amalgam $W^{p,q}(\mathbb{R}^{d})\;(1\leqslant p<\infty ,1\leqslant q<2)$. We have shown $T_{F}$ maps $W^{p,1}(\mathbb{R}^{d})$ to $W^{p,q}(\mathbb{R}^{d})$ if and only if $F$ is real analytic on $\mathbb{R}^{2}$ and $F(0)=0$. Similar result is proved in the case of modulation spaces $M^{p,q}(\mathbb{R}^{d})$. In particular, this gives an affirmative answer to the open question proposed in Bhimani and Ratnakumar (J. Funct. Anal. 270(2) (2016), 621–648).
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2015 ◽
Vol 13
(01)
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pp. 1550003
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2009 ◽
Vol 80
(1)
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pp. 105-116
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2017 ◽
Vol 9
(4)
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pp. 881-890
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Keyword(s):
2011 ◽
Vol 228
(5)
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pp. 2943-2981
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2012 ◽
Vol 2012
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pp. 1-8
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2011 ◽
Vol 60
(4)
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pp. 1203-1228
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