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We obtain an atomic decomposition for weighted Triebel–Lizorkin spaces on spaces of homogeneous type, using the area function, the discrete Calderón reproducing formula and discrete sequence spaces.
Wiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates
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