Abstract
We use the concept of moduli of continuity to give some generalised characterisation theorems in some generalised Hölder type spaces of functions over \({\mathbb {R}}\), characterising certain Lipschitz type conditions on functions in terms of their Fourier transforms. Our main results are inspired by a theorem of Titchmarsh, combined with the notion of moduli of continuity, for characterising Jacobi–Lipschitz conditions in \(L^2({\mathbb {R}}^+, d\mu (t))\) using approximation by a generalised translation operator.
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Joel E. Restrepo was supported in parts by the Nazarbayev University program 091019CRP2120.
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Daher, R., Fernandez, A. & Restrepo, J.E. Characterising Extended Lipschitz Type Conditions with Moduli of Continuity. Results Math 76, 125 (2021). https://doi.org/10.1007/s00025-021-01433-2
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DOI: https://doi.org/10.1007/s00025-021-01433-2
Keywords
- generalized Hölder space
- Lipschitz type condition
- Fourier transform
- modulus of continuity
- Jacobi transform
- generalized translation operator