Sobolev inequalities with symmetry

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Weighted Strichartz estimates with angular regularity and their applications (2008, background): “(1 − ∆M) 1 2 , then, from (1.7), we can get the following estimate, (1.8) rn−1 2 kf(ry)kL∞ y∈M .kΛs Mfk B˙ 1 2 2,1 with s > n−1 2 . This vastly relaxes the condition s > n− 3 2 of Cho and Ozawa [5] in the case of M = Sn−1. As an application of (1.5) and (1.8), we can get the following result o”
Blowup ofH1solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation (2017, background): “To do this, we recall the following radial Sobolev embedding ([25, 5]).”
On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity (2012, unknown): “Let us invoke from [9] that the embedding H α 2 rad →֒ L is compact if n ≥ 2, 1 < α < 2 and 2 < r < 2n n−α .”
Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, unknown): “As shown in Cho and Ozawa [13], for general s ∈ (0, 1), we do not have a similar radial lemma in Hs r (R3).”