Fourier Transforms of Lipschitz Functions and Fourier Multipliers on Compact Groups.
Tong-Seng Quek, Leonard Y.H. Yap (1983)
Mathematische Zeitschrift
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Tong-Seng Quek, Leonard Y.H. Yap (1983)
Mathematische Zeitschrift
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A.S. Besicovitch (1929)
Mathematische Zeitschrift
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Walter R. Bloom (1981)
Mathematische Zeitschrift
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J.M. Anderson (1976)
Mathematische Zeitschrift
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Dr. L. C., Cambridge (England) Young (1938)
Mathematische Zeitschrift
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Robert Fraser (1970)
Fundamenta Mathematicae
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Graham H. Williams (1977)
Mathematische Zeitschrift
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R.K.S. Rathore (1975)
Mathematische Zeitschrift
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Adam Parusiński (2005)
Annales Polonici Mathematici
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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.
Itai Benjamini, Alexander Shamov (2015)
Analysis and Geometry in Metric Spaces
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It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
O.Carruth McGehee (1979)
Mathematische Annalen
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Tadeusz Mostowski (2004)
Banach Center Publications
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Ferenc Móricz (2010)
Studia Mathematica
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We consider complex-valued functions f ∈ L¹(ℝ), and prove sufficient conditions in terms of f to ensure that the Fourier transform f̂ belongs to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes zyg(α) and zyg(α) for some 0 < α ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary in the case of real-valued functions f for which either xf(x) ≥ 0 or f(x) ≥ 0 almost everywhere.
Younis, M.S. (1992)
International Journal of Mathematics and Mathematical Sciences
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Walter R. Bloom (1982)
Colloquium Mathematicae
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Ferenc Móricz (2008)
Colloquium Mathematicae
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We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if for all...