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2 results

  • SCHRÖDINGER PROPAGATOR ON WIENER AMALGAM SPACES IN THE FULL RANGE

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  • GUOPING ZHAO, WEICHAO GUO
  • Journal:
    Nagoya Mathematical Journal , First View
    Published online by Cambridge University Press:
    27 August 2024, pp. 1-17
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  • Using the technique of Gabor analysis, we characterize the boundedness of $e^{i\Delta }: W^{p_1,q_1}_m\rightarrow W^{p_2,q_2}$ with modulation and translation operators, where and m is a v-moderate weight. The sharp exponents for the boundedness are also characterized in the case of power weight.

  • SHARPNESS OF SOME PROPERTIES OF WIENER AMALGAM AND MODULATION SPACES

  • Part of
  • ELENA CORDERO, FABIO NICOLA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 1 / August 2009
    Published online by Cambridge University Press:
    19 June 2009, pp. 105-116
    Print publication:
    August 2009
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  • We prove sharp estimates for the dilation operator f(x)⟼f(λx), when acting on Wiener amalgam spaces W(Lp,Lq). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces Mp,q, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.