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BOUNDEDNESS OF THE SPECTRA OF BASE FUNCTIONS FOR NEW SPACES

  • Received : 2019.12.31
  • Accepted : 2019.01.14
  • Published : 2020.02.15

Abstract

We investigate the boundedness of the spectrum of a convex base function for a new function space. The result guarantees the continuity of the Calderón-Zygmund operators on the new space.

Keywords

References

  1. R. Adams, Sobolev spaces, 2nd Edition, Academic press, Amsterdam, 2003.
  2. H-C. Pak, Existence of solutions for a nonlinear elliptic equation with general flux term, Fixed Point Theory and Appl., 2011 (2011), Article ID 496417.
  3. H-C. Pak and S-H. Chang, A new function space $L_{\alpha}(X)$- Version 1.1, J. Chungcheong Math. Soc., 21 (2008), 471-481.
  4. H-C. Pak and S-H. Chang, Poincare's inequality on a new function space $L_{\alpha}(X)$, J. Chungcheong Math. Soc., 22 (2009), 309-318.
  5. H-C. Pak and Y-J. Park, Trace operator and a nonlinear boundary value problem in a new space, Boundary Value Problems, 2014 (2014), 2014:153.
  6. H-C. Pak and Y-J. Park, Spectrum and Singular Integrals on a New Weighted Function Space, Acta Mathematica Sinica, English Series, 34 (2018), no. 11, 1692-1702. https://doi.org/10.1007/s10114-018-7043-8