Functiones et Approximatio Commentarii Mathematici

Wavelet characterization of the pointwise multiplier space $\dot{{X}_{r}$

Yoshihiro Sawano and Sadek Gala

Full-text: Open access

Abstract

In the present note we characterize the function space $\dot{X}_{r}$, which is the set of pointwise multipliers which map $L^{2}$ into $\dot{H}^{-r}$. To this end, we use wavelets and capacity.

Article information

Source
Funct. Approx. Comment. Math., Volume 43, Number 2 (2010), 109-116.

Dates
First available in Project Euclid: 9 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1291903392

Digital Object Identifier
doi:10.7169/facm/1291903392

Mathematical Reviews number (MathSciNet)
MR2767165

Zentralblatt MATH identifier
1213.42081

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol s kii-type inequalities)

Keywords
pointwise multiplier wavelet decomposition

Citation

Gala, Sadek; Sawano, Yoshihiro. Wavelet characterization of the pointwise multiplier space $\dot{{X}_{r}$. Funct. Approx. Comment. Math. 43 (2010), no. 2, 109--116. doi:10.7169/facm/1291903392. https://projecteuclid.org/euclid.facm/1291903392


Export citation

References

  • V.G. Maz'ya and T.O. Shaposhnikova, Theory of Multipliers in Spaces of Differentiable Functions, Monographs and Studies in Mathematics 23, Pitman, 1985.
  • V.G. Maz'ya and T.O. Shaposhnikova, Theory of Sobolev multipliers with applications to differential and integral operators, Springer-Verlag, Berlin, 2009.
  • I. Daubechies, Ten Lectures on Wavelets.
  • Y. Meyer, Ondelettes et opérateurs, Paris : Hermann, 1990.
  • Y. Sawano, Wavelet characterization of Besov Triebel-Lizorkin-Morrey spaces, Functiones et Approximatio, 38 (2008), 7--21.