Abstract
In this chapter we are motivated by the right side of (⋆) to give an exploration of the fundamental characteristics of the Gauss-Sobolev spaces which will be used to introduce the Gaussian Sobolev p-capacity later in Chapter 3
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Bibliography
L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics (CRC, Boca Raton, 1992)
I. Gentil, Logarithmic Sobolev inequality for diffusion semigroups, in Optimal Transportation. London Mathematical Society Lecture Note Series, vol. 413 (Cambridge University Press, Cambridge, 2014), pp. 41–57
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Liu, L., Xiao, J., Yang, D., Yuan, W. (2018). Gaussian Sobolev p-Space. In: Gaussian Capacity Analysis. Lecture Notes in Mathematics, vol 2225. Springer, Cham. https://doi.org/10.1007/978-3-319-95040-2_1
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DOI: https://doi.org/10.1007/978-3-319-95040-2_1
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