Fefferman--Stein-type estimates and fractional NLS in Fourier Sobolev spaces

2026/07/20 by Divyang G. Bhimani, Ryosuke Hyakuna
#math.AP

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Abstract

In this paper, we prove a sharp Fefferman--Stein-type estimate for the fractional Schrödinger equation, which can be regarded as a generalized Strichartz estimate for data in the Fourier Lebesgue space \widehatL^p. Then, as an application of the Fefferman--Stein inequality and its off-diagonal generalization, we prove large data local well-posedness and small data global well-posedness results for the one dimensional fractional nonlinear Schrödinger equation with pure power nonlinearities in the homonegeneous and inhomogeneous Fourier--Sobolev spaces \widehatH^s_p,\widehatH^s_p. Solutions are established in L_x^r(ℝ ;L^q_t(I)) spaces in order to overcome the difficulty of a loss of derivatives in the standard Strichartz estimates.

Citations

• Nonlinear fractional Schrödinger equations in one dimension

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