Advanced Search
Article Contents
Article Contents

Characterization of function spaces via low regularity mollifiers

Abstract Related Papers Cited by
  • Smoothness of a function $f:\mathbb{R}^n\to\mathbb{R}$ can be measured in terms of the rate of convergence of $f*\rho_{\epsilon}$ to $f$, where $\rho$ is an appropriate mollifier. In the framework of fractional Sobolev spaces, we characterize the "appropriate" mollifiers. We also obtain sufficient conditions, close to being necessary, which ensure that $\rho$ is adapted to a given scale of spaces. Finally, we examine in detail the case where $\rho$ is a characteristic function.
    Mathematics Subject Classification: Primary: 46E35.


    \begin{equation} \\ \end{equation}
  • [1]

    G. Bourdaud, Ondelettes et espaces de Besov, Rev. Mat. Iberoamericana, 11 (1995), 477-512.doi: 10.4171/RMI/181.


    L. Grafakos, Classical Fourier Analysis, 2nd edition, Graduate Texts in Mathematics, 249, Springer, New York, 2008.


    E. Stein, An $H^{1}$ function with nonsummable Fourier expansion, in Harmonic Analysis (Cortona, 1982), Lecture Notes in Math., 992, Springer, Berlin, 1983, 193-200.doi: 10.1007/BFb0069159.


    E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, With the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III, Princeton Mathematical Series, 43, Princeton University Press, Princeton, NJ, 1993,


    E. Stein, M. Taibleson and G. Weiss, Weak type estimates for maximal operators on certain $H^p$ classes, in Proceedings of the Seminar on Harmonic Analysis (Pisa, 1980), 1, 1981, 81-97.


    H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Mathematical Library, 18, North-Holland Publishing Co., Amsterdam, 1978.


    H. Triebel, Theory of Function Spaces, Monographs in Mathematics, 78, Birkhäuser Verlag, Basel, 1983.doi: 10.1007/978-3-0346-0416-1.


    H. Triebel, Theory of Function Spaces. II, Monographs in Mathematics, 84, Birkhäuser Verlag, Basel, 1992.doi: 10.1007/978-3-0346-0419-2.

  • 加载中

Article Metrics

HTML views() PDF downloads(44) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint