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- W2008952794 abstract "In this article we study the Fourier and the horocyclic Radon transform on harmonic <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper N upper A> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>NA</mml:annotation> </mml:semantics> </mml:math> </inline-formula> groups (also known as Damek-Ricci spaces). We consider the geometric Fourier transform for functions on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-spaces and prove an analogue of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-restriction theorem. We also prove some mixed norm estimates for the Fourier transform generalizing the Hausdorff-Young and Hardy-Littlewood-Paley inequalities. Unlike Euclidean spaces the domains of the Fourier transforms are various strips in the complex plane. All the theorems are considered on these entire domains of the Fourier transforms. Finally we deal with the existence of the Radon transform on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-spaces and obtain its continuity property." @default.
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- W2008952794 date "2009-03-16" @default.
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- W2008952794 title "Fourier and Radon transform on harmonic 𝑁𝐴 groups" @default.
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- W2008952794 doi "https://doi.org/10.1090/s0002-9947-09-04800-4" @default.
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