Boundedness of Eisenstein integrals on split rank one semisimple symmetric spaces
Abstract
We characterise the bounded left K-invariant normalized Eisenstein integrals on split rank one semisimple symmetric spaces. As a consequence we prove Hausdorff-Young inequality on these spaces. We also prove similar result for K-finite Eisenstein integrals on pseudo-Riemannian real hyperbolic spaces.
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