measure of a Brownian motion (see [@morters2010brownian], for example), which is continuous. The corresponding process when $s\in (0,1)$ is an isotropic $2s$-stable Lévy motion, which is a jump process.

Acknowledgements {#acknowledgements .unnumbered}
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The authors would like to thank David Jerison, Jason Miller, and Charles Smart for helpful discussions. Scott Sheffield thanks the astronomer John M. Kovac for conversations about early universe cosmology and for the corresponding references. Sheffield would also like to thank Bertrand Duplantier, Rémi Rhodes, and Vincent Vargas, his co-authors on a survey of the log-correlated Gaussian field [@duplantier2013log] for a broad range of useful insights.

Preliminaries {#sec:preliminaries}
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In this section we remind the reader of some definitions and facts regarding tempered distributions and homogeneous Sobolev spaces. Some of the following notation and ideas are from [@triebel1983theory], to which we refer the reader for more discussion on homogeneous spaces. We will introduce and construct several linear spaces. To aid the reader in keeping track of the various definitions, we include a glossary of these definitions in the on page .

Tempered Distributions and Sobolev spaces {#subsec:tempdist}
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Fix a positive integer $d$, and denote by ${\mathcal{S}}({\mathbb{R}}^d)$ the real Schwartz space, defined to be the set of 