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2013, De Gruyter studies in mathematics, ISBN 9783110263404, Volume 49, xi, 372
Book
2014, De Gruyter studies in mathematics, ISBN 9783110281231, Volume 52., xiii, 449
Book
Nonlinear Analysis, ISSN 0362-546X, 08/2018, Volume 173, pp. 146 - 153
The main purpose of this paper is to prove some generalized Gagliardo–Nirenberg interpolation inequalities involving the Lorentz spaces Lp,α, BMO and the... 
Lipschitz space | Gagliardo–Nirenberg’s inequality | Lorentz spaces | BMO | Fractional Sobolev space | Gagliardo–Nirenberg's inequality
Journal Article
2012, 1, Annals of mathematics studies, ISBN 9780691153551, Volume no. 179, ix, 425
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into... 
Calculus of variations | Functional analysis | Banach spaces | Mathematics | Math | Frechet spaces | Lipschitz spaces
Book
中国科学:数学英文版, ISSN 1674-7283, 2015, Volume 58, Issue 2, pp. 309 - 388
Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0〈p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈... 
Weiss | Hardy空间 | 测度空间 | 幽门螺杆菌 | 分数次积分 | Campanato空间 | 应用 | ATB | molecular block | Campanato space | Lipschitz space | Mathematics | 30L99 | non-homogeneous metric measure space | ρ -weakly doubling measure | 42B35 | 42B30 | 42B20 | Calderón-Zygmund operator | Applications of Mathematics | atomic block | Hardy space | Non-homogeneous metric measure space | ρ-weakly doubling measure | Atomic block | Molecular block
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 8/2018, Volume 15, Issue 4, pp. 1 - 19
In this paper, we give some new characterizations of the Lipschitz spaces via the boundedness of commutators associated with the fractional maximal operator,... 
commutator | 42B35 | 42B25 | Generalized Orlicz–Morrey spaces | fractional maximal operator | Calderón–Zygmund operator | 42B20 | Mathematics, general | Mathematics | Lipschitz spaces | Riesz potential | MATHEMATICS | MATHEMATICS, APPLIED | Calderon-Zygmund operator | Generalized Orlicz-Morrey spaces | HARDY-SPACES | SINGULAR INTEGRAL-OPERATORS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2015, Volume 425, Issue 1, pp. 71 - 84
We compare Besov spaces Bp,q0,b with zero classical smoothness and logarithmic smoothness b defined by using the Fourier transform with the corresponding... 
Limiting interpolation spaces | Logarithmic smoothness | Lipschitz spaces | Besov spaces | MATHEMATICS, APPLIED | NUMBERS | SOBOLEV | FUNCTION PARAMETER | MATHEMATICS | LORENTZ | FUNCTORS | GENERALIZED SMOOTHNESS | REAL INTERPOLATION | ENTROPY
Journal Article
Mathematische Annalen, ISSN 0025-5831, 2018, Volume 373, Issue 3-4, pp. 1017 - 1056
The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is... 
DISTRIBUTIONS | MATHEMATICS | LIPSCHITZ-SPACES | EUCLIDEAN N-SPACE
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2018, Volume 275, Issue 8, pp. 2059 - 2095
We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are:–the... 
Metric measure space | Warped product | Sobolev space | MATHEMATICS | METRIC MEASURE-SPACES | LIPSCHITZ FUNCTIONS | RICCI CURVATURE
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 12/2009, Volume 19, Issue 4, pp. 1017 - 1028
We prove the differentiability of Lipschitz maps X → V, where X denotes a PI space, i.e. a complete metric measure space satisfying a doubling condition and a... 
doubling measure | differentiability | metric measure space | Mathematics | Radon-Nikodym property | minimal upper gradient | 30L99 | Banach space | Poincaré inequality | 30L05 | Analysis | Lipschitz function | 58C20 | Differentiability | Metric measure space | Doubling measure | Minimal upper gradient | MATHEMATICS | Poincare inequality
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2019, Volume 16, Issue 6, pp. 1 - 26
Journal Article
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9939, 07/2019, Volume 147, Issue 7, pp. 3057 - 3060
We prove the result stated in the title. This provides a first example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to the... 
FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | Pelczynski space | Lipschitz free space | APPROXIMATION PROPERTY
Journal Article
Journal of the ACM (JACM), ISSN 0004-5411, 08/2019, Volume 66, Issue 4, pp. 1 - 77
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 8, pp. 2697 - 2727
We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show... 
Lipschitz functions | Lipschitz-free spaces | Orlicz spaces | Carnot groups | MATHEMATICS | SEPARATED NETS | THEOREM | PROPERTY | METRICS | GROWTH | Analysis | Numerical analysis
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 7/2015, Volume 12, Issue 3, pp. 973 - 986
We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also... 
46B28 | proper metric space | Primary 46B10 | Mathematics, general | Mathematics | Secondary 46B04 | bounded approximation property | ultrametric space | duality | Lipschitz-free space | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | LIPSCHITZ-FREE SPACES | APPROXIMATION PROPERTIES
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 08/2016, Volume 13, Issue 4, pp. 1893 - 1906
We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to a"" (1). This extends results of... 
46B03 | 46B15 | 54E35 | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | ultrametric space | APPROXIMATION PROPERTIES | Schauder basis | Lipschitz-free space | Mathematics - Functional Analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 260, Issue 11, pp. 3299 - 3362
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 11/2013, Volume 10, Issue 4, pp. 2007 - 2025
We introduce a new type of variable exponent function spaces  Ḣ p(·),q(·),α(·)( $${\mathbb{R}^n}$$ ) and H p(·),q(·),α(·)( $${\mathbb{R}^n}$$ ) of Herz type,... 
Morrey spaces | maximal function | Function spaces | Primary 46E30 | sublinear operators | Mathematics, general | Herz spaces | Mathematics | variable exponent spaces | Secondary 47B38 | singular operators | MATHEMATICS, APPLIED | BOUNDEDNESS | POTENTIALS | FOURIER-TRANSFORMS | INTEGRALS | MATHEMATICS | SINGULAR-OPERATORS | SUBLINEAR-OPERATORS | LIPSCHITZ SPACES
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 08/2018, Volume 57, Issue 4
We prove that if the dimension of the first cohomology group of a space is N, then the space is a flat torus. This generalizes a classical result due to... 
METRIC-MEASURE-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | LIPSCHITZ FUNCTIONS | EXAMPLES | RICCI CURVATURE
Journal Article
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