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Pitt and Boas inequalities for Fourier and Hankel transforms |
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| Authors: | L De Carli D Gorbachev S Tikhonov |
| Institution: | 1. Florida International University, Department of Mathematics, Miami, FL 33199, USA;2. Tula State University, Department of Mechanics and Mathematics, 300600 Tula, Russia;3. ICREA and Centre de Recerca Matemàtica, Apartat 50 08193 Bellaterra, Barcelona, Spain |
| Abstract: | We prove Pitt and Boas inequalities for products of radial functions and spherical harmonics in Rn. In the process, we obtain upper and lower estimates of the operator norm of the Hankel transform with power weights. Our inequalities are sharp in some specific cases. |
| Keywords: | Fourier and Hankel transforms Sharp constants Pitt inequalities Boas inequalities |
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