Abstract
In this paper, we obtain an isometry between the Fock–Sobolev space and the Gauss–Sobolev space with the same order. As an application, we use multipliers on the Gauss–Sobolev space to characterize the boundedness of an integral operator on the Fock–Sobolev space.
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References
Bogachev, V.L.: Gaussian Measure. American Mathematical Society, Providence (1998)
Berger, C.A., Coburn, L.A.: Toeplitz operators and quantum mechanics. J. Funct. Anal. 48, 273–299 (1985)
Berger, C.A., Coburn, L.A.: Heat flow and Berezin–Toeplitz estimates. Am. J. Math. 116, 563–590 (1994)
Cho, H., Zhu, K.: Fock–Sobolev space and their Carleson measure. J. Funct. Anal. 263, 2483–2506 (2012)
Cao, G., Li, J., Shen, M., Wick, B.D., Yan, L.: A boundedness criterion for singular integral of convolution type of the Fock space. Adv. Math. 363, 107001 (2020)
Liu, L., Xiao, J., Yang, D., Yuan, W.: Gaussian Capacity Analysis. Springer, Berlin (2018)
López, I.A.P.: Sobolev spaces and potential spaces associated to Hermite polynomials expansions. Extr. Math. 33, 229–249 (2018)
Maz’ya, V.G., Shaposhnikova, T.O.: Theory of Sobolev Multipliers. Springer, Berlin (2012)
Mitkovski, M., Wick, B.D.: A reproducing kernel thesis for operators on Bergman-type spaces. J. Funct. Anal. 267, 2028–2055 (2014)
Poornima, S.: Multiplier of Sobolev spaces. J. Funct. Anal. 45, 1–28 (1982)
Stein, E., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971)
Urbina-Romero, W.: Gaussian Harmonic Analysis. Springer, Berlin (2018)
Zhu, K.: Operator Theory Function Spaces. Dekker, New York (1990)
Zhu, K.: Analysis on Fock Spaces. Springer, New York (2012)
Zhu, K.: Singular integral operators on the Fock space. Integral Equ. Oper. Theory 81, 451–454 (2015)
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Brett D. Wick’s research is supported in part by a National Science Foundation DMS Grants # 1560955 and # 1800057 and Australian Research Council—DP 190100970. Shengkun Wu’s research is supported in part by China Scholarship Council (201906050022) and the National Natural Science Foundation of China (11531003, 11701052)
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Wick, B.D., Wu, S. Integral Operators on Fock–Sobolev Spaces via Multipliers on Gauss–Sobolev Spaces. Integr. Equ. Oper. Theory 94, 22 (2022). https://doi.org/10.1007/s00020-022-02701-8
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DOI: https://doi.org/10.1007/s00020-022-02701-8