Why are Sobolev spaces labelled W^{s,p}?

Discussion in 'Math Research' started by Arnold Neumaier, Mar 16, 2006.

  1. Arnold Neumaier

    Arnold Neumaier Guest

    Does anyone know the significance of the letter W
    in the natation W^{s,p} for Sobolev spaces of functions whose
    weak derivatives up to s-th order are in L^p?


    Arnold Neumaier
     
    Arnold Neumaier, Mar 16, 2006
    #1

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  2. Arnold Neumaier

    PAVEL DUBOVSKIY Guest

    As far as I know, Sobolev's notation is W_p^s. I do not know why in american
    literature "p" was moved to the upper index. Also, I do not know why did
    Sobolev use "W".

    -Pavel Dubovski
     
    PAVEL DUBOVSKIY, Mar 29, 2006
    #2

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  3. Arnold Neumaier

    Giuseppe Guest

    I guess "W" stands for "weak", because such spaces are defined in terms
    of weak derivatives.
    I think that the position of the p follows the tradition of putting it
    as upper index in L^p spaces.

    Giuseppe
     
    Giuseppe, Mar 29, 2006
    #3
  4. Arnold Neumaier

    renardym Guest

    I have seen the speculation that W stands for weak, but Sobolev wrote
    in Russian. As far as I know,
    Sobolev gave no reason for chosing W.
     
    renardym, Mar 29, 2006
    #4

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