We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.
In this paper we continue the study of the Fourier transform on , , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of , where is the number of equal angles considered in . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of , , of fixed eccentricity...
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
For a wavelet ψ of compact support, we define a square function and a maximal function NΛ. We then obtain the equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.