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Register a new userQualitative uncertainty principles for the windowed Opdam--Cherednik transform on weighted modulation spaces
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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 uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based o
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In this paper, we introduce the Hausdorff operator associated with the Opdam--Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam--Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.
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 strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with regular weights is given. As applications, our result improves the results of Siskakis, A. G. cite{AG1} and K{o}nig, W. cite{K} and answers a question of Siskakis, A. G. proposed in cite{AG4}. We also characterize strongly continuous semigroups of weighted composition operators on weighted Bergman spaces in terms of abelian intertwiners of multiplication operator $M_z$.
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