Browsing Harmonic Analysis by Subject "Bourgain's counterexample"

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Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick

Eceizabarrena, D.; Ponce Vanegas, F. (2021-12-09)

We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol

Eceizabarrena, D.; Ponce Vanegas, F. (2021-08-24)

We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...