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Space filling with metric measure spaces

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We show a sharp relationship between the existence of space filling mappings with an upper gradient in a Lorentz space and the Poincaré inequality in a general metric setting. As key examples, we consider these phenomena in Cantor diamond spaces and the Heisenberg groups.

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Correspondence to K. Wildrick.

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The first author was supported by Academy of Finland grants 120972 and 128144.

The second author was partially supported by the Swiss National Science Foundation and Academy of Finland grant 120972.

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Wildrick, K., Zürcher, T. Space filling with metric measure spaces. Math. Z. 270, 103–131 (2012).

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