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Generalized inhomogeneous Strichartz estimates

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  • We prove new inhomogeneous generalized Strichartz estimates, which do not follow from the homogeneous generalized estimates by virtue of the Christ-Kiselev lemma. Instead, we make use of the bilinear interpolation argument worked out by Keel and Tao and refined by Foschi presented in a unified framework. Finally, we give a sample application.

    Mathematics Subject Classification: Primary: 35B45; Secondary: 35Q55.

    Citation:

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  • Figure 1.  This pictorial representation generalizes [7,Figure 2,p.5]. The axes refer to the spatial integrability coefficients. The rectangle $ABCD$ corresponds to estimates found from factorization and the application of the Christ-Kiselev lemma up to endpoints. The origin relates to the dispersive estimate; one finds local estimates to hold in the wedge $AOCD$ by virtue of interpolation, restrictions on global estimates cut off estimates with too large spatial integrability coefficients

    Figure 2.  We give a pictorial representation similar to [3,Figure 1,p.1907]. In the setting of [3,Corollary 1.,p.1907] we find $A=(\frac{n-a}{2n},\frac{1}{2}), \, B= (\frac{n}{n+a}-\frac{n}{2(n+1)},\frac{n}{n+a}-\frac{n}{2(n+1)}), \, C=(\frac{n}{2(n+1)},\frac{n}{2(n+1)}), \, D=(\frac{1}{2},0)$, where the open line $\overline{BC}$ corresponds to the range from [3,Theorem 1.2.,p.1908] and the closed line $\overline{AD}$ corresponds to estimates found from factorization and application of the Christ-Kiselev lemma

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