\`x^2+y_1+z_12^34\`
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.

    Citation:

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

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

    [2]

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

    [3]

    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.

    [4]

    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,

    [5]

    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.

    [6]

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

    [7]

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

    [8]

    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
SHARE

Article Metrics

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

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return