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2015, New mathematical monographs, ISBN 9781107092341, Volume 27, xii, 434
.... Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality... 
Sobolev spaces | Metric spaces
Book
Probability Theory and Related Fields, ISSN 0178-8051, 09/2009, Volume 145, Issue 1-2, pp. 285 - 322
We consider the space of complete and separable metric spaces which are equipped with a probability measure... 
Gromov metric triple | Gromov-Hausdorff topology | Wasserstein metric | Weak topology | Λ-Coalescent | Prohorov metric | Metric measure spaces | ℝ-trees | weak topology | STATISTICS & PROBABILITY | R-trees | Lambda-Coalescent | Studies | Probability
Journal Article
Duke mathematical journal, ISSN 0012-7094, 2014, Volume 163, Issue 7, pp. 1405 - 1490
In this paper, we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X, d, m... 
MATHEMATICS | SOBOLEV SPACES | TRANSPORT | INEQUALITIES | STABILITY | COMPACT ALEXANDROV SPACES | FINSLER MANIFOLDS | WASSERSTEIN SPACES | HEAT-FLOW | GRADIENT FLOWS | GEOMETRY | 60J65 | 35K05
Journal Article
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 ∈ ∈(0... 
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
Inventiones mathematicae, ISSN 1432-1297, 2013, Volume 195, Issue 2, pp. 289 - 391
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces $(X,\mathsf {d},\mathfrak {m... 
52C23 | 49J52 | 35K90 | Mathematics, general | Mathematics | 58J35 | 49Q20 | 31C25 | EXISTENCE | MATHEMATICS | EQUATIONS | CURVATURE CONDITIONS | GEOMETRY | Mathematical analysis | Dirichlet problem | Calculus | Heat transmission | Entropy | Density | Curvature | Heat transfer
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2015, Volume 367, Issue 7, pp. 4661 - 4701
é condition. This more general class of spaces includes Euclidean spaces endowed with Lebesgue measure, complete noncompact Riemannian manifolds with bounded geometry and the pointed metric measure limits... 
MATHEMATICS | DIMENSION CONDITION | LIPSCHITZ FUNCTIONS | HEAT-FLOW | GEOMETRY | Differential Geometry | Metric Geometry | Mathematics
Journal Article
Acta mathematica, ISSN 0001-5962, 2006, Volume 196, Issue 1, pp. 65 - 131
We introduce and analyze lower (Ricci) curvature bounds $ \underline{{Curv}} {\left( {M,d,m} \right)} $  ⩾ K for metric measure spaces... 
Mathematics, general | Mathematics | Manifolds | Metric space | Mathematical analysis | Transportation | Isomorphism | Entropy | Curvature | Estimates | Optimization
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2019, Volume 69, Issue 1, pp. 207 - 223
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2014, Volume 34, Issue 4, pp. 1641 - 1661
We prove that the linear "heat" flow in a RCD(K, infinity) metric measure space (X, d, m) satisfies a contraction property with respect to every L-p-Kantorovich-Rubinstein-Wasserstein distance, p is an element... 
Γ-calculus | Dirichlet forms | Ricci curvature | Metric-measure spaces | Optimal transport | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | INEQUALITY | optimal transport | FOKKER-PLANCK EQUATIONS | MATHEMATICS | metric-measure spaces | MANIFOLDS | Gamma-calculus | GEOMETRY
Journal Article
Forum mathematicum, ISSN 1435-5337, 2011, Volume 25, Issue 4, pp. - - -
Journal Article
Potential analysis, ISSN 1572-929X, 2018, Volume 51, Issue 1, pp. 127 - 146
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations... 
53C23 | 51F99 | Probability Theory and Stochastic Processes | 31E05 | Mathematics | 30L99 | Conformal transformation | Metric measure space | Ricci tensor | Geometry | Potential Theory | Functional Analysis | Bakry-Émery theory | Curvature-dimension condition | MATHEMATICS | Bakry-Emery theory | RICCI CURVATURE
Journal Article
Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 04/2018, Volume 104, Issue 2, pp. 162 - 194
Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour... 
and phrases Hardy spaces | Riesz transforms | heat kernel estimates | metric measure spaces | MATHEMATICS | LOCAL DIRICHLET SPACES | BOUNDS | Hardy spaces | OPERATORS
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2015, Volume 31, Issue 2, pp. 497 - 530
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2015, Volume 111, Issue 5, pp. 1071 - 1129
The aim of this paper is to discuss convergence of pointed metric measure spaces in the absence of any compactness condition... 
EXISTENCE | MATHEMATICS | TANGENT-CONES | RIEMANNIAN-MANIFOLDS | UNIQUENESS | GEOMETRY | Equivalence | Mathematical analysis | Heat transmission | Spectra | Formulas (mathematics) | Curvature | Heat transfer | Convergence
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 05/2015, Volume 103, Issue 5, pp. 1228 - 1275
The main result of this article states that the (K,N)-cone over some metric measure space satisfies the reduced Riemannian curvature-dimension condition RCD⁎(KN,N+1... 
Curvature-dimension condition | Cone | Metric measure space | Maximal diameter | LOCAL DIRICHLET SPACES | MATHEMATICS, APPLIED | LIPSCHITZ FUNCTIONS | RICCI CURVATURE | MATHEMATICS | SOBOLEV SPACES | PRODUCTS | BOUNDS | RIGIDITY | GEOMETRY
Journal Article
Abstract and applied analysis, ISSN 1085-3375, 9/2013, Volume 2013, pp. 1 - 8
The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral... 
FRACTIONAL INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | HARDY-SPACES | BOUNDEDNESS | COMMUTATORS | CALDERON-ZYGMUND OPERATORS | POTENTIALS | NON-DOUBLING MEASURES | ANALYTIC CAPACITY | SEMIADDITIVITY | Metric spaces | Research | Integrals | Mathematical research | Operator theory | Operators
Journal Article
2011, ISBN 1405183691, xvi, 375
"A Probability Metrics Approach to Financial Risk Measures relates the field of probability metrics and risk measures to one another and applies them to finance for the first time... 
Financial risk management | Probabilities
Book
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2019, Volume 21, Issue 6, pp. 1809 - 1854
We prove that a metric measure space (X, d, m) satisfying finite-dimensional lower Ricci curvature bounds and whose Sobolev space W(1,2... 
MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | rectifiable space | unique tangent space | Ricci curvature | optimal transport | GEOMETRY
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 464, Issue 1, pp. 707 - 724
.... Motivated by recent work on barycentric maps on spaces of probability measures on ordered Banach spaces, we introduce and study a stochastic order on the space of probability measures P(X... 
Ordered metric space | Borel probability measure | AGH mean inequalities | Normal cone | Stochastic order | Wasserstein metric | MATHEMATICS | MATHEMATICS, APPLIED | BARYCENTRIC MAPS
Journal Article