A variational nonlinear Hausdorff-Young inequality in the discrete setting

Following the works of Lyons and Oberlin, Seeger, Tao, Thiele and Wright, we relate the variation of certain discrete curves on the Lie group $\text{SU}(1,1)$ to the corresponding variation of their linearized versions on the Lie algebra. Combining this with a discrete variational Menshov-Paley-Zygmund theorem, we establish a variational Hausdorff-Young inequality for a discrete version of the nonlinear Fourier transform on $\text{SU}(1,1)$.Comment: 16 page

Combining hyaluronic acid with chitosan enhances gene delivery

The low gene transfer efficiency of chitosan-DNA polyplexes is a consequence of their high stability and consequent slow DNA release. The incorporation of an anionic polymer is believed to loosen chitosan interactions with DNA and thus promote higher transfection efficiencies. In this work, several formulations of chitosan-DNA polyplexes incorporating hyaluronic acid were prepared and characterized for their gene transfection efficiency on both HEK293 and retinal pigment epithelial cells. The different polyplex formulations showed morphology, size, and charge compatible with a role in gene delivery. The incorporation of hyaluronic acid rendered the formulations less stable, as was the goal, but it did not affect the loading and protection of the DNA. Compared with chitosan alone, the transfection efficiency had a 4-fold improvement, which was attributed to the presence of hyaluronic acid. Overall, our hybrid chitosan-hyaluronic acid polyplexes showed a significant improvement of the efficiency of chitosan-based nonviral vectors in vitro, suggesting that this strategy can further improve the transfection efficiency of nonviral vectors.Fundacao para a Ciencia e Tecnologia [SFRH/BD/52424/2013]; Marie Curie Reintegration Grant [PIRG-GA-2009-249314

A variational restriction theorem

We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal Fourier restriction theory.Comment: 10 pages, v2: bibliography is updated, a short survey of the maximal Fourier restriction is include

Chitosan-Hyaluronic acid hybrid vectors for retinal gene therapy

info:eu-repo/semantics/publishedVersio

A sharp nonlinear Hausdorff-Young inequality for small potentials

The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the exponent. We show that the nonlinear Hausdorff-Young quotient admits an even better upper bound than the linear one, provided that the function is sufficiently small in the $L^1$ norm. The proof combines perturbative techniques with the sharpened version of the linear Hausdorff-Young inequality due to Christ.Comment: 14 pages, v2: referee's suggestions incorporate