Characterising Extended Lipschitz Type Conditions with Moduli of Continuity
Daher R. Fernandez A. Restrepo J.E.
August 2021Birkhauser
Results in Mathematics
2021#76Issue 3
We use the concept of moduli of continuity to give some generalised characterisation theorems in some generalised Hölder type spaces of functions over 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 L2(R+, dμ(t)) using approximation by a generalised translation operator.
Fourier transform , generalized Hölder space , generalized translation operator , Jacobi transform , Lipschitz type condition , modulus of continuity
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Laboratory T.A.G.M.D, Faculty of Sciences Ain Chock, Casablanca, Morocco
Department of Mathematics, Eastern Mediterranean University, Northern Cyprus, via Mersin-10, Famagusta, Turkey
Regional mathematical center, Southern Federal University, Rostov-on-Don, Russian Federation
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Laboratory T.A.G.M.D
Department of Mathematics
Regional mathematical center
Department of Mathematics
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