The Boas problem on Hankel transforms. (English) Zbl 1428.42007
Summary: Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas-type results involving real-valued general monotone functions are obtained. Corresponding results for the Fourier transform are also given.
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |
| 26D15 | Inequalities for sums, series and integrals |
| 26A48 | Monotonic functions, generalizations |
Keywords:
Boas conjecture; Hankel transform; general monotonicity; weighted Lebesgue spaces; Lorentz spacesReferences:
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