A Survey on Isometries Between Lipschitz Spaces

Associative and Non-Associative Algebras and Applications - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-030-35256-1_3 ◽

2020 ◽

pp. 51-88

Author(s):

M. G. Cabrera-Padilla ◽

A. Jiménez-Vargas ◽

Moisés Villegas-Vallecillos

Keyword(s):

Lipschitz Spaces

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Mean Lipschitz spaces and a generalized Hilbert operator

Collectanea mathematica ◽

10.1007/s13348-018-0217-y ◽

2018 ◽

Vol 70 (1) ◽

pp. 59-69 ◽

Cited By ~ 3

Author(s):

Noel Merchán

Keyword(s):

Lipschitz Spaces ◽

Generalized Hilbert Operator ◽

Hilbert Operator ◽

Mean Lipschitz Spaces

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Behavior of Bi-Cubic Functions in Lipschitz Spaces

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080218060136 ◽

2018 ◽

Vol 39 (6) ◽

pp. 803-808 ◽

Cited By ~ 1

Author(s):

Ismail Nikoufar

Keyword(s):

Lipschitz Spaces

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On the unique predual problem for Lipschitz spaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004117000597 ◽

2017 ◽

Vol 165 (3) ◽

pp. 467-473 ◽

Cited By ~ 7

Author(s):

NIK WEAVER

Keyword(s):

Banach Space ◽

Metric Space ◽

Lipschitz Spaces

AbstractFor any metric space X, the predual of Lip(X) is unique. If X has finite diameter or is complete and convex—in particular, if it is a Banach space—then the predual of Lip0(X) is unique.

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Lipschitz Spaces and Bernstein's Theorem on Absolutely Convergent Fourier Transforms*

Indiana University Mathematics Journal ◽

10.1512/iumj.1969.18.18024 ◽

1968 ◽

Vol 18 (4) ◽

pp. 283-323 ◽

Cited By ~ 11

Author(s):

C. Herz

Keyword(s):

Fourier Transforms ◽

Lipschitz Spaces

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Multiplier Representations of Sequence Spaces with Applications to Lipschitz Spaces and Spaces of Functions of Generalized Bounded Variation

Linear Spaces and Approximation / Lineare Räume und Approximation ◽

10.1007/978-3-0348-7180-8_22 ◽

1978 ◽

pp. 235-245

Author(s):

Günther Goes

Keyword(s):

Bounded Variation ◽

Sequence Spaces ◽

Lipschitz Spaces

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Some results on isometric composition operators on Lipschitz spaces

Revista Matemática Complutense ◽

10.1007/s13163-021-00410-1 ◽

2021 ◽

Author(s):

Abraham Rueda Zoca

Keyword(s):

Convex Hull ◽

Composition Operator ◽

Metric Spaces ◽

Composition Operators ◽

Extreme Points ◽

Necessary Condition ◽

Closed Convex Hull ◽

Lipschitz Spaces ◽

Complete Characterisation

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.

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