SPHERICAL AVERAGED ENDPOINT STRICHARTZ ESTIMATES FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH INVERSE SQUARE POTENTIAL

摘要

We investigate the two-dimensional Schr¨odinger equation with repulsiveninverse square potential, and we prove the following homogeneous endpoint Strichartznestimate:nu0002uu0002L2tn(L∞r Lθ) ≤ Cu0002u0u0002L2 ,nwhere L∞r Lθ is a norm that applies L2 average on the angular variable, first, and thennthe supremum on the radial variable.