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Gaussian Campanato (p, κ)-Class

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2225))

Abstract

In this chapter we are motivated by the left side of (⋆) to investigate the Campanato (p, κ)-class on \(\mathbb{G}^{n}\) and its relationship with the Morrey space, John-Nirenberg space, and Lipschitz space on \(\mathbb{G}^{n}\).

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Bibliography

  1. A.E. Gatto, W. Urbina, On Gaussian Lipschitz spaces and the boundedness of fractional integrals and fractional derivatives on them. Quaest. Math. 38, 1–25 (2015)

    Article  MathSciNet  Google Scholar 

  2. A.E. Gatto, E. Pineda, W. Urbina, Riesz potentials, Bessel potentials, and fractional derivatives on Besov-Lipschitz spaces for the Gaussian measure, in Recent Advances in Harmonic Analysis and Applications. Springer Proceedings in Mathematics and Statistics, vol. 25 (Springer, New York, 2013), pp. 105–130

    Google Scholar 

  3. L. Liu, P. Sjögren, A characterization of the Gaussian Lipschitz space and sharp estimates for the Ornstein-Uhlenbeck Poisson kernel. Rev. Mat. Iberoam. 32, 1189–1210 (2016)

    Article  MathSciNet  Google Scholar 

  4. L. Liu, Y. Sawano, D. Yang, Morrey-type spaces on Gauss measure spaces and boundedness of singular integrals. J. Geom. Anal. 24, 1007–1051 (2014)

    Article  MathSciNet  Google Scholar 

  5. G. Mauceri, S. Meda, BMO and H1 for the Ornstein-Uhlenbeck operator. J. Funct. Anal. 252, 278–313 (2007)

    Article  MathSciNet  Google Scholar 

  6. E. Pineda, W. Urbina, Some results on Gaussian Besov-Lipschitz spaces and Gaussian Triebel-Lizorkin spaces. J. Approx. Theory 161, 529–564 (2009)

    Article  MathSciNet  Google Scholar 

  7. P. Sjögren, Operators associated with the Hermite semigroup - a survey. J. Fourier Anal. Appl. 3, 813–823 (1997)

    Article  MathSciNet  Google Scholar 

  8. E.M. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, NJ, 1970), xiv+290 pp.

    Google Scholar 

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Liu, L., Xiao, J., Yang, D., Yuan, W. (2018). Gaussian Campanato (p, κ)-Class. In: Gaussian Capacity Analysis. Lecture Notes in Mathematics, vol 2225. Springer, Cham. https://doi.org/10.1007/978-3-319-95040-2_2

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