Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LIPSCHITZ TYPE CHARACTERIZATION OF FOCK TYPE SPACES

  • Hong Rae, Cho (Department of Mathematics Pusan National University) ;
  • Jeong Min, Ha (Department of Mathematics Pusan National University)
  • Received : 2021.10.27
  • Accepted : 2022.06.15
  • Published : 2022.11.30
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Abstract

For setting a general weight function on n dimensional complex space ℂn, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

Keywords

Acknowledgement

The first author was financially supported by NRF-2020R1F1A1A0104860111 and the second author was financially supported by NRF-2021R1A2B5B03087097.

References

  1. H. R. Cho, J. M. Ha, and H.-W. Lee, A Sobolev norm equivalence on Fock-type spaces with a mixed norm, Complex Var. Elliptic Equ. 65 (2020), no. 6, 986-1000. https://doi.org/10.1080/17476933.2019.1641494
  2. H. R. Cho, J. M. Ha, and K. Nam, Characterizations for the Fock-type spaces, Bull. Korean Math. Soc. 56 (2019), no. 3, 745-756. https://doi.org/10.4134/BKMS.b180540
  3. B. R. Choe and K. Nam, New characterizations for the weighted Fock spaces, Complex Anal. Oper. Theory 13 (2019), no. 6, 2671-2686. https://doi.org/10.1007/s11785-018-0850-1
  4. O. Constantin and J. Pelaez, Integral operators, embedding theorems and a LittlewoodPaley formula on weighted Fock spaces, J. Geom. Anal. 26 (2016), no. 2, 1109-1154. https://doi.org/10.1007/s12220-015-9585-7
  5. J. M. Ha, H. R. Cho, and H.-W. Lee, A norm equivalence for the mixed norm of Fock type, Complex Var. Elliptic Equ. 61 (2016), no. 12, 1644-1655. https://doi.org/10.1080/17476933.2016.1197916
  6. S. Li, H. Wulan, R. Zhao, and K. Zhu, A characterisation of Bergman spaces on the unit ball of Cn, Glasg. Math. J. 51 (2009), no. 2, 315-330. https://doi.org/10.1017/S0017089509004996
  7. S. Li, H. Wulan, and K. Zhu, A characterization of Bergman spaces on the unit ball of Cn. II, Canad. Math. Bull. 55 (2012), no. 1, 146-152. https://doi.org/10.4153/CMB2011-047-6
  8. M. Pavlovic and J. A. Pelaez, Weighted integrals of higher order derivatives of analytic functions, Acta Sci. Math. (Szeged) 72 (2006), no. 1-2, 73-93.
  9. M. Pavlovic and J. A. Pelaez, An equivalence for weighted integrals of an analytic function and its derivative, Math. Nachr. 281 (2008), no. 11, 1612-1623. https://doi.org/10.1002/mana.200510701
  10. H. Wulan and K. Zhu, Lipschitz type characterizations for Bergman spaces, Canad. Math. Bull. 52 (2009), no. 4, 613-626. https://doi.org/10.4153/CMB-2009-060-6