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Cartan Covers and Doubling Bernstein-Type Inequalities on Analytic Subsets of ℂ 2 $$\mathbb {C}^2$$

In: Analysis at Large

Author

Listed:
  • Michael Goldstein

    (University of Toronto, Department of Mathematics)

  • Wilhelm Schlag

    (Yale University, Department of Mathematics
    The University of Chicago, Department of Mathematics)

  • Mircea Voda

    (The University of Chicago, Department of Mathematics
    University of Toronto, Department of Mathematics)

Abstract

We prove a version of the doubling Bernstein inequalities for the trace of an analytic function of two variables on an analytic subset of ℂ 2 $$\mathbb {C}^2$$ . The estimate applies to the whole analytic set in question including its singular points. The proof relies on a version of the Cartan estimate for maps in ℂ 2 $$\mathbb {C}^2$$ which we establish in this work.

Suggested Citation

  • Michael Goldstein & Wilhelm Schlag & Mircea Voda, 2022. "Cartan Covers and Doubling Bernstein-Type Inequalities on Analytic Subsets of ℂ 2 $$\mathbb {C}^2$$," Springer Books, in: Artur Avila & Michael Th. Rassias & Yakov Sinai (ed.), Analysis at Large, pages 101-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-05331-3_5
    DOI: 10.1007/978-3-031-05331-3_5
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