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2 results

  • Beltrami Equation with Coefficient in Sobolev and Besov Spaces

  • Victor Cruz, Joan Mateu, Joan Orobitg
  • Journal:
    Canadian Journal of Mathematics / Volume 65 / Issue 6 / 01 December 2013
    Published online by Cambridge University Press:
    20 November 2018, pp. 1217-1235
    Print publication:
    01 December 2013
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  • Our goal in this work is to present some function spaces on the complex plane $\mathbb{C},\,X(\mathbb{C})$, for which the quasiregular solutions of the Beltrami equation, $\bar{\partial }f(z)\,=\,\mu (z)\partial f(z)$, have first derivatives locally in $X(\mathbb{C})$, provided that the Beltrami coefficient $\mu $ belongs to $X(\mathbb{C})$.

  • є-Families of Operators in Triebel-Lizorkin and Tent Spaces

  • Grant Welland, Shiying Zhao
  • Journal:
    Canadian Journal of Mathematics / Volume 47 / Issue 5 / 01 October 1995
    Published online by Cambridge University Press:
    20 November 2018, pp. 1095-1120
    Print publication:
    01 October 1995
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  • In this paper, we study the boundedness of є-families of operators on Triebel-Lizorkin with wide range of parameters. We also prove that є -families of operators are bounded from Triebel-Lizorkin spaces into (generalized) tent spaces, and obtain a characterization of certain Triebel-Lizorkin spaces in terms of tent spaces. In particular, the boundedness of fractional operators in Triebel-Lizorkin, and a sharp version of T\theorem for generalized Calderón-Zygmund operators on Triebel-Lizorkin spaces can be considered as applications of (proofs of) these results.