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This paper is devoted to give several characterizations on a more general level for the boundedness of $tau$-Wigner distributions acting from weighted modulation spaces to weighted modulation and Wiener amalgam spaces. As applications, sharp exponents are obtained for the boundedness of $tau$-Wigner distributions on modulation spaces with power weights. We also recapture the main theorems of Wigner distribution obtained in cite{CorderoNicola2018IMRNI,Cordero2020a}. As consequences, the characterizations of the boundedness on weighted modulation spaces of several types of pseudodifferential operators are established. In particular, we give the sharp exponents for the boundedness of pseudodifferential operators with symbols in Sj{o}strands class and the corresponding Wiener amalgam spaces.
We characterize the (essentially) decreasing sequences of positive numbers $beta$ = ($beta$ n) for which all composition operators on H 2 ($beta$) are bounded, where H 2 ($beta$) is the space of analytic functions f in the unit disk such that $infty$
We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<infty$ of the Hankel operators $H_ f$ and $H_{bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.
We give sufficient conditions for compactness of localization operators on modulation spaces $textbf{M}^{p,q}_{m_{lambda}}( mathbb{R}^{d})$ of $omega$-tempered distributions whose short-time Fourier transform is in the weighted mixed space $L^{p,q}_{m_lambda}$ for $m_lambda(x)=e^{lambdaomega(x)}$.
We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the
The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain the Cowling--Prices, Hardys and Morgans