Concentration of Product Spaces

Abstract We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.

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Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type

Journal of Functional Analysis ◽

10.1016/j.jfa.2016.05.002 ◽

2016 ◽

Vol 271 (7) ◽

pp. 1793-1843 ◽

Cited By ~ 4

Author(s):

Anna Kairema ◽

Ji Li ◽

M. Cristina Pereyra ◽

Lesley A. Ward

Keyword(s):

Function Spaces ◽

Homogeneous Type ◽

Metric Measure Spaces ◽

Product Spaces ◽

Spaces Of Homogeneous Type ◽

Structure Theorems ◽

Measure Spaces

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Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

Journal of Functional Analysis ◽

10.1016/j.jfa.2017.01.001 ◽

2017 ◽

Vol 272 (8) ◽

pp. 3311-3346 ◽

Cited By ~ 6

Author(s):

Alexander Grigor'yan ◽

Eryan Hu ◽

Jiaxin Hu

Keyword(s):

Dirichlet Forms ◽

Heat Kernels ◽

Metric Measure Spaces ◽

Measure Spaces ◽

Non Local

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Jump processes and nonlinear fractional heat equations on metric measure spaces

Mathematische Nachrichten ◽

10.1002/mana.200310352 ◽

2006 ◽

Vol 279 (1-2) ◽

pp. 150-163 ◽

Cited By ~ 5

Author(s):

Jiaxin Hu ◽

Martina Zähle

Keyword(s):

Jump Processes ◽

Heat Equations ◽

Metric Measure Spaces ◽

Measure Spaces

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Rigidity properties of smooth metric measure spaces via the weighted $p$-Laplacian

Proceedings of the American Mathematical Society ◽

10.1090/proc/13285 ◽

2016 ◽

Vol 145 (3) ◽

pp. 1287-1299 ◽

Cited By ~ 1

Author(s):

Nguyen Thac Dung

Keyword(s):

Metric Measure Spaces ◽

Smooth Metric Measure Spaces ◽

Measure Spaces

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A note on the extension of BV functions in metric measure spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2007.07.039 ◽

2008 ◽

Vol 340 (1) ◽

pp. 197-208 ◽

Cited By ~ 7

Author(s):

Annalisa Baldi ◽

Francescopaolo Montefalcone

Keyword(s):

Metric Measure Spaces ◽

Bv Functions ◽

Measure Spaces

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Well-posedness of Lagrangian flows and continuity equations in metric measure spaces

Analysis & PDE ◽

10.2140/apde.2014.7.1179 ◽

2014 ◽

Vol 7 (5) ◽

pp. 1179-1234 ◽

Cited By ~ 24

Author(s):

Luigi Ambrosio ◽

Dario Trevisan

Keyword(s):

Well Posedness ◽

Metric Measure Spaces ◽

Continuity Equations ◽

Measure Spaces

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Lower bound of coarse Ricci curvature on metric measure spaces and eigenvalues of Laplacian

Geometriae Dedicata ◽

10.1007/s10711-013-9844-3 ◽

2013 ◽

Vol 169 (1) ◽

pp. 99-107 ◽

Cited By ~ 2

Author(s):

Yu Kitabeppu

Keyword(s):

Lower Bound ◽

Ricci Curvature ◽

Metric Measure Spaces ◽

Measure Spaces ◽

Coarse Ricci Curvature

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Discretization of integrals on compact metric measure spaces

Advances in Mathematics ◽

10.1016/j.aim.2021.107602 ◽

2021 ◽

Vol 381 ◽

pp. 107602

Author(s):

Martin D. Buhmann ◽

Feng Dai ◽

Yeli Niu

Keyword(s):

Metric Measure Spaces ◽

Measure Spaces

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Fractional operators of variable order from variable exponent Morrey spaces to variable exponent Campanato spaces on quasi-metric measure spaces with growth condition

Ricerche di Matematica ◽

10.1007/s11587-021-00639-4 ◽

2021 ◽

Author(s):

Humberto Rafeiro ◽

Stefan Samko

Keyword(s):

Growth Condition ◽

Variable Exponent ◽

Morrey Spaces ◽

Variable Order ◽

Fractional Operators ◽

Metric Measure Spaces ◽

Measure Spaces

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Two open problems in the fixed point theory of contractive type mappings on quasimetric spaces

Carpathian Journal of Mathematics ◽

10.37193/cjm.2017.02.04 ◽

2017 ◽

Vol 33 (2) ◽

pp. 169-180

Author(s):

MITROFAN M. CHOBAN ◽

◽

VASILE BERINDE ◽

◽

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Partial Answer ◽

Open Problems ◽

Complete Answer ◽

Contractive Type ◽

Generalized Distances

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., Generalized distances and their associate metrics. Impact on fixed point theory, Creat. Math. Inform., 22 (2013), No. 1, 23–32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.

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